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Question 720143: please help me solve the following trigonometric equation using Pythagorean identity formula:
1-sin^2theta=0.5
Click here to see answer by ikleyn(52963)

Question 1210421: Consider the trigonometric function f(t) = 2 + 3 sin(4π(t − 1)).
(a) What is the amplitude of f(t)?
(b) What is the period of f(t)?
(c) What are the maximum and minimum values attained by f(t)?
(d) Sketch the graph of f(t) for t ∈ [−1, 1].
Click here to see answer by ikleyn(52963)

Question 578708: find the angle(s) that would make each statement true.
theta equals arc csc (sqrt of 2)
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Question 488238: sin 2x + cos 60 = 0, 0 < x < 360.
i have been able to find out that sin inverse of -1/2 is -30, but how do i find answers in the 3rd and fourth quadrant for 2x?? then i can find x. my answers are coming wrong, and i can apply no suitable rule. please help, and show working if possible.
Click here to see answer by ikleyn(52963)

Question 554415: Sorry i'm not sure if this is the right category for this question but its for year 12 specialist maths and is on reciprocal circular functions.
the question is sketch the graph of each of the following reciprocal circular function over the given domain
, the < are supposed to be greater than or equal to signs

i'm not quite sure how to find the dilation factor for one and for two i know that the period is 2pie/b but is b 1 or is it pie/2??
Click here to see answer by ikleyn(52963)

Question 1167299: The function graphed is of the form y=cos x + c, y=sin x + c, y=cos(x-d), or y= sin(x-d), where d is the least possible positive value. Determine the equation of the graph .
Click here to see answer by ikleyn(52963)

Question 1160369: Find a root of an equation f(x)=2coshxsinx-1 taking initial value x0=0.4, using Newton Raphson method correct up to four decimal places.
Do all the calculations.
Click here to see answer by ikleyn(52963)

Question 1169789: Given a right pyramid ABCDE, on a square base ABCD, with AB = 8 cm, and height EO = 5 cm, what are the values of the following:
(a) angle EAB
(b) angle β between a slant edge and the plane on the base.
(c) angle θ between a slant face and the plane on the base.
Click here to see answer by ikleyn(52963)

Question 1176289: A 6-string guitar is being strummed by a guitarist once. When he strummed the strings, he hit the 6th string
(topmost string) first and released it before hitting the 5th string consequently. The 6th string went back to its initial
position after 50 milliseconds from its initial position. When the 6th string reaches its maximum point, the 5th string
went back to its normal position for the first time. Assume an equal tension applied to both strings.
A. Find the equation of the 6th string and graph.
B. Find the equation of the 5th string and graph.
1. Assume that the 5th string is released when the 6th string went back to its initial position for the first time.
2. Assume that the oscillation of the 5th string started when the 6th string reached its maximum point.
Click here to see answer by ikleyn(52963)

Question 1177187: Owen is jumping on a trampoline. When his feet hit the deck of the trampoline, the material depresses to a minimum height of 2cm. On average, Owen is reaching a maximum height of 200cm every 10 seconds. Determine the equation of a sinusoidal function that would model this situation, assuming Owen reaches his first maximum at 6 seconds.
Click here to see answer by ikleyn(52963)

Question 1179653: https://gyazo.com/848645a235363970dae8196a58a2bbdc
Click here to see answer by ikleyn(52963)

Question 1182678: The area bounded by y = 3, x = 2, y = -3 and x = 0 is revolved about the y-axis.
The moment of inertia of the solid is
Click here to see answer by ikleyn(52963)

Question 1121000: Solve the system:
Click here to see answer by mccravyedwin(412)

Question 1210270: Figure 12.36 shows a cross-section of a sheet of corrugated iron.

The sheet is a series of arcs of radius 10 cm., each arc subtending 120^o at its centre.
If there are 14 such arcs in one sheet, how wide would the sheet be if flattened out?
Click here to see answer by Edwin McCravy(20067)

Question 1210259: Triangle ABC has side lengths AB = 8, BC = 10, and AC = 12. Find \dfrac{\cos A}{\cos B}.
Click here to see answer by greenestamps(13219)

Question 1210259: Triangle ABC has side lengths AB = 8, BC = 10, and AC = 12. Find \dfrac{\cos A}{\cos B}.
Click here to see answer by ikleyn(52963)

Question 1210261: Acute triangle ABC has \sin A = \dfrac{2}{5} and \sin B = \dfrac{2}{\sqrt{7}}. What is \sin C?
Click here to see answer by math_tutor2020(3822)

Question 1210261: Acute triangle ABC has \sin A = \dfrac{2}{5} and \sin B = \dfrac{2}{\sqrt{7}}. What is \sin C?
Click here to see answer by ikleyn(52963)

Question 1210238: -5pi/8 radians
Find a coterminal angle between 0 and 2pm for each given angle
Click here to see answer by greenestamps(13219)

Question 1210238: -5pi/8 radians
Find a coterminal angle between 0 and 2pm for each given angle
Click here to see answer by ikleyn(52963)

Question 1168158: A cross-country race covers a course which takes shape of a triangle, KLM. Runners are to start at K and run 4 km due north to a point L.
From L, they are to run 5 km on a bearing of 300° to a point, M, and then run directly to K.
(a) draw a diagram to represent the triangular course carefully labeling:
(i) the points K, L and M
(II) the distances 4 km and 5 km
(iii) the north direction
(iv) the bearing 300°
(b) determine, using your diagram:
(i) the distance KM in km
(ii) the bearing of M from K
Click here to see answer by CPhill(1987)

Question 1168437: A ship travels on a N 28o E course. The ship travels until it is due north of a port which is 200 nm due east of the port from which the ship originated.
How far did the ship travel?
Click here to see answer by CPhill(1987)

Question 1168441: Two Coast Guard stations, A and B, are on an east-west line and are 115 km apart. The bearing of a ship from station A is N 18o E, and the bearing of the same ship from station B is N 33o W.
a) How far is the ship from the east-west line connecting the two Coast Guard stations.
b) How far is the ship from station A?
c) How far is the ship from station B?

Click here to see answer by CPhill(1987)

Question 1210192: Find an acute angle A such that \sin 4A = \sin A + \sin 2A. Express your answer in degrees.
Click here to see answer by ikleyn(52963)

Question 1210192: Find an acute angle A such that \sin 4A = \sin A + \sin 2A. Express your answer in degrees.
Click here to see answer by CPhill(1987)

Question 1168835: On at 550m hole, steve'a tee shoot goes 195m and is 21 degrees to the right of the direct path to the flag. The second shot flies 13 degrees to the right of the new direction toward the flag. but only travels 160m. How far is steve's golfball from the flag? show the steps of your solution and diagram

Click here to see answer by CPhill(1987)

Question 1169042: using a scale diagram , sketch and determine the resultant vector
a) 7m ( down) and 9 m (left)
b) 6km (N55degreesW) and 4 km (E35degreesS)

Click here to see answer by CPhill(1987)

Question 1169043: Using trigonometry determine the resultant vector
a) 8m [N] and 12 m [W]
b) 15N [30degreesSofE] and 8 N [E]
Click here to see answer by CPhill(1987)

Question 1168194: An overhead crane is suspended from a ceiling by two chains. One chain is 4.6 m long and forms an angle of 60^\circ with the ceiling. The other chain is 6.4 m long. What angle does the larger chain make with the ceiling?
Click here to see answer by ikleyn(52963)

Question 1210134: In \triangle PQR, we have \angle P = 90^\circ, PQ=3, and QR = 5. Find \tan R.
Click here to see answer by ikleyn(52963)

Question 1210134: In \triangle PQR, we have \angle P = 90^\circ, PQ=3, and QR = 5. Find \tan R.
Click here to see answer by CPhill(1987)

Question 1210135: Find AC in the diagram to the nearest integer.

(You will need to use a calculator. Make sure to use "Degree" instead of "Radian" as the angle unit when computing trigonometric functions.)

AB = 31, angle A = 90 degrees, angle B = 50 degrees
Click here to see answer by math_tutor2020(3822)

Question 1165349: A person’s resting blood pressure is 116 over 88. This means that the blood pressure oscillates between a maximum of 116 and a minimum of 88. The person’s resting heart rate is 60 beats per minute. Let P represent the blood pressure and t represent the time in seconds. Write the equation for the blood pressure P as a function of time t seconds.
Click here to see answer by ikleyn(52963)

Question 1169601: England. Like everything else, the ticket prices to Six Flags continue to increase every year. Because of this, your family is planning to buy a family membership this year that includes reduced admission costs, discounts on food and drinks, free parking and “skip the line” passes every time you visit.
Your parents have asked you to determine which membership plan would be best for your family. The table below summarizes the three membership options:
O1 Gold membership: $225 per visit
O2 Platinum Membership: Original payment of $750 plus $100 every visit.
O3 Diamond Membership: You pay an initial membership fee of $1575. On your first visit you pay $25, on your second visit you pay $50 and on your third visit you pay $75. This constant rate of change applies to every visit you make.
Let C represent the cost function and let v represent the number of visits to Six Flags you make during the summer months. Write a linear function in slope intercept form for each membership option. Is there a y-intercept for each option? What is the rate of change for each option? Use the variables identified in the word problem to write the equations.

Click here to see answer by CPhill(1987)

Question 1170014: Suppose sin x =2/7,cos x > 0, sin y = − 2/5 and cos y < 0. Then
cos x=
cos y=
Find each of the following quantities:
sin(x+y)=
Cos(x+y)=
Tan(x+y)=
Click here to see answer by CPhill(1987)

Question 1170350: Have no idea where to even begin to solve this problem. Any help is appreciated.
The Grand Canyon Skywalk at Eagle Point is a horseshoe shaped steel frame with a glass floor looking down to the Grand Canyon below. The Skywalk extends 70 feet over the canyon rim and is 10 feet wide. The walkway consists of a semicircle with a straight portion on each side
Path Width 10 feet 65 feet Outer Circle: 65 feet diameter Location of Light Tower .Inner Circle. 45 feet diameter 70 feet
A light tower is going to be installed on the left edge of the Skywalk .
The light will shine down to the opposite edge of the Skywalk
How tall does the light tower need to be if the angle of depression is 51°? (Round to 1 decimal place and be sure to include units.)
Click here to see answer by CPhill(1987)

Question 1170415: a man sitting on 22.5 m high storey building measures the angles of elevation of a telecom mast directly ahead of him as 43°. He measures the angle of elevation of the mast when he is 52m in the front of the building on the horizontal ground as 70°
A calculate the height of the mast
The distance between the building and the mast.
Click here to see answer by CPhill(1987)

Question 1170695: Given that I0=10−12 watts/meter2, what is the intensity of a sound for which the decibel level of the sound measures 121? Round off your answer to three decimal places.
Click here to see answer by CPhill(1987)

Question 1170834: The angle between the coastline and
Johnson’s boat at the first lighthouse is 43°
From the second lighthouse, the angle between the coastline and Johnson’s boat is 55° How much shorter is the direct distance from the boat to the second lighthouse than the direct distance to the first lighthouse? [4]

Click here to see answer by CPhill(1987)

Question 1170877: Consider the following.
t=-2pi/3
(a) Find the reference number t for the value of t.
t =

(b) Find the terminal point determined by t.
(x, y) =

Click here to see answer by CPhill(1987)

Question 1171107: A commercial jet travels from Miami to Seattle. The jet's velocity with respect to the air is 585 miles per hour, and its bearing is 332°. The jet encounters a wind with a velocity of 50 miles per hour from the southwest.
1. Write the velocity of the wind as a vector in component form.
2. Write the velocity of the jet relative to the air in component form.
3. What is the speed of the jet with respect to the ground? (Round your answer to one decimal place.) (mph)
4. What is the true direction of the jet? (Round your answer to one decimal place.)
N ____ degrees W
Click here to see answer by CPhill(1987)

Question 1209871: Find the value of each trigonometric ratios. Simplify fractions to simplest terms
HYP=29
OPP=21
ADJ=20
Click here to see answer by CPhill(1987)

Question 1171512: For each of the following, tell how many non-congruent triangles PQR fit the given
description, and find the size of angle Q. Make a separate diagram for each case.
(a) p = 3, q = 5, angle P = 27 degrees
(b) p = 8, q = 5, angle P = 57 degrees
(c) p = 7, q = 8, angle P = 70 degrees
(d) p = 10, q = 20, angle P = 30 degrees

Click here to see answer by CPhill(1987)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380