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Question 1160774: The formula D=24[1-(cos^-1(tan(i)tan(theta))/pi] can be used to approximate the number of hours of daylight D when the declination of the Sun is i(degree) at a location of theta(degree) north latitude for any date between the vernal equinox and autumnal equinox. The declination of the Sun is defined as the angle i(degree) between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle theta(degree) between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth. To use the formula both i(degree) and theta(degree) must be expressed in radians.
Approximate the number of hours of daylight in Houston, Texas for the following dates: (a.) April 2nd, (b.) September 12th, and (c.) June 28th. (Write your answer in the form of hours and minutes)
Sun Declination
a is N4 42'
b is N4 25'
c is N23 19'
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Question 1160776: The formula D=24[1-(cos^-1(tan(i)tan(theta))/pi] can be used to approximate the number of hours of daylight D when the declination of the Sun is i(degree) at a location of theta(degree) north latitude for any date between the vernal equinox and autumnal equinox. The declination of the Sun is defined as the angle i(degree) between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle theta(degree) between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth. To use the formula both i(degree) and theta(degree) must be expressed in radians.
Approximate the number of hours of daylight in Quito, Ecuador for the following dates A) June 20 B) March 21st C) May 3rd
A = N23 26'
B = 0 00'
C = N15 30'

Click here to see answer by CPhill(2303)

Question 1160777: The formula D=24[1-(cos^-1(tan(i)tan(theta))/pi] can be used to approximate the number of hours of daylight D when the declination of the sun is i(degree) at a location of theta(degree) north latitude for any date between the vernal equinox and autumnal equinox. The declination of the Sun is defined as the angle i(degree) between the equatorial plane and any ray of light from the Sun. The latitude of a location is the angle(theta(degree)) between the Equator and the location on the surface of Earth, with the vertex of the angle located at the center of Earth. To use the formula both i and theta must be expressed in radians.
(a.) Determine the north latitude of the Arctic Circle and then Approximate the number of hours of daylight at the Arctic Circle for the following dates: (b.) Summer Solstice, (c.) Vernal Equinox (i.e. March 21st), and (d.) May 3rd. (Write your answer in the form of hours and minutes) (e.) The number of hours on the Winter Solstice may be found by computing the number of hours of daylight on the Summer Solstice and subtracting this result from 24 hours, due to the symmetry of the orbital path of Earth around the Sun. Compute the number of hours of daylight for the Arctic Circle on the Winter Solstice. What do you conclude about daylight for a location on the Arctic Circle?
B) June 21st: N23 26'
C) N66.5 23.5'
D) N15 30'

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Question 1157552: An Uber driver leaves home and drives 1.2km to the East to pick up a passenger. She drives 3.4km to the South and drops off the passenger. Calculate the distance (in km) and direction (as a true bearing) for the driver to return directly home.
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Question 180061: Determine exact values.
Find sin A and cos A if tan A=5/3 and cos A <0.
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Question 180062: Find sin B and cot B if cosB=-1/4 and tan B>0.
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Question 211804: if a=22, b=14, and c=30, find the area of triangle ABC.
a)33 sq units
b)121.0 sq units
c)130.2 sq units
d)143.8 sq units
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Question 211794: in triangle ABC, A=47 degrees,b=12,c=8.find a to the nearest tenth
a)6.3
b)8.7
c)8.8
d)18.4
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Question 211809: change 29pi/37 radians to degree measure
a)5220 degrees
b)141.1 degrees
c)167.6 degrees
d)66.6 degrees
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Question 207935: Given a point (5,-5) on the terminal side of angle0, find the value of sin.
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Question 212348: Find all angles t such that 3t is coterminal with 180 degrees and t is between 0 degrees and 360 degrees.
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Question 212322: Draw the angle in quadrant II whose terminal side is on 1/2x + y = 0.
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Question 197454: Solve for x in the equation (1 +sinx/cosx)+(cosx/1+sinx)=4 for 0≤ x ≤ 2π rad.
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Question 207286: If the latitude of Chicago is about 42 degrees and the radius of the earth is about 4000 miles, how far is Chicago from the equator? ( use pi= 3.1416)

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Question 937255: Solve the following for 0 < x < 2pi
(sin x + cos x)^2 = 1
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Question 101945: Solve each of the following systems by substitution. I am having major problems with these kind of problems...HELP, ZACK
5x - 2y= -5
1 y - 5x = 3
8x - 4y = 16
y = 2x - 4
This last problem the 4y and the y in the next prblem line up buy it isnt turning out like that before i submit it
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Question 940505: Determine the amplitude period and phase shift of y = -2 cos(pi x -3)
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Question 942251: cos(2θ+20)=sin(3θ−10)

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Question 942249: tan(θ)=cot(4θ+20)
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Question 944548: Solve the equation 4 times cosine of theta plus 1 = 2 times cosine of theta fortheta greater than or equal to 0 but less than 2 pi..
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Question 944480: Solve for all 0 degrees less than or equal to x less than 360 degrees.
3tan x- sqrt( 3 )=0
2sin x cos x=2sin x
cos^2 x-sin^2 x + 3cos x - 1=0
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Question 949907: Find all values of t in the interval [0, 2π] satisfying the given equation. (Enter your answers as a comma-separated list.)
(4 cot t)^2 = 48

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Question 950272: Solve the equation for t on the interval [0,2π) 4 cos t - 4 sin t = 4
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Question 951003: find all solution of the equation, and find the fundamental solutions on the interval
[0, 2pi] tan x= -sqrt3
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Question 1158473: An isosceles trapezoid has a height of 4cm and bases 3cm and 7cm long. How long are its diagonals? Use the law of cosines.
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Question 958122: How many revolution per second will an automobile wheel make at the rate of 63.4km per hour if the diameter is 5.4dm??p
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Question 958122: How many revolution per second will an automobile wheel make at the rate of 63.4km per hour if the diameter is 5.4dm??p
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Question 958763: how do you find the exact value of the expression
cos(sin^-1 1/3 - tan^-1 1/2)
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Question 958870: Find all solutions of the following equation: tan (theta/8) +sqrt3 = 0. find the solutions in the interval [0, 2pi]

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Question 959220: Find exact Value of tan Beta/2, Given that tanBeta = square root 5/2 and pi < Beta < 3pi/2
So I think Beta/2 is in quadrant 3 making it positive but I tried square root of 5 as the answer and thats wrong please help!!!!
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Question 1158099: Please help me answer this question:
Simplify
sin ( - θ) sin (90θ + θ) - cos (180 θ - θ) cos (270 θ +θ).
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Question 1158051: if sec(t) = -5 and the terminal point of t is in quadrant iii, use the identity sin^2(t/2)=1-cos(t)/2 to find the exact value of (sin(t/2)+cos(t))
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Question 960664: determine if it is possible for a number t to satisfy the given conditions sint=5/13 and cost=12/13
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Question 961016: If sin A= -1/squareroot of 5 with A in QII, find sin 2A.
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Question 961016: If sin A= -1/squareroot of 5 with A in QII, find sin 2A.
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Question 962783: Use trigonometric identities to solve sin(theta)+(sqrt3)sin(theta)=0 exactly for 0 is less than or equal to theta which is less than 2pi;. If there is more than one answer, enter your answers as a comma separated list.
Thank you
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Question 963379: Find the solutions of the equation that are in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
cos 2u − cos u = 0
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Question 963649: Please solve this equation exactly.
sin(arccos(3/5) - arctan(5/12)) =
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Question 968978: if sine theta = -4/7 and is in quadrant 3, then the sum of sine theta + sine (theta-pie)+sine(2pie+theta) is?
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Question 969216:
i. find the domain of g in interval form
ii. find the x-intercept(s) of the graph of g

(iii) In what quadrant does the terminal side of an angle of 5 radians lie? justify your answer
(iv) Find all solutions for the equation:
Thank you
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Question 1158028: determine the specified trigonometric ratio for each angle with a terminal side that passes through the given point.
1.Sin0; (-8,6)
2.csc0; (2,-1)
3.tan0;(0,1)
4.cos0; (-4,-2)
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Question 970477: Evaluate cos[arctan(-5/12)].
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Question 970477: Evaluate cos[arctan(-5/12)].
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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, 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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, 25381..25425, 25426..25470