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Question 730613: From the top of a 210-ft lighthouse, the angle of depression to a ship in the ocean is 15 degrees. How far is the ship from the base of the lighthouse?
A. 874ft
B. 478ft
C. 784ft
D. 748ft
Click here to see answer by ikleyn(53427)

Question 1162547: Write the partial fraction decomposition of the following rational expression.

Click here to see answer by MathTherapy(10587)

Question 730721: Can you help me prove this trigonometic identity?:
(sinƟcosƟ)/(cos^2Ɵ-sin^2Ɵ)=tanƟ/(1-tan^2Ɵ)

Click here to see answer by ikleyn(53427)

Question 731899: approximate the solution to tan θ on the interval [0,2pi)
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Question 1165816: 1. Draw an angle with the given measure in standard position.
a.70° b. 300° c. 570° d. -450° e. -185°
1. Rewrite each degree measure in radians and each radians measure in degrees.
a. 3π/4 b.π/6 c.19π/3

2.The Earth rotates on its axis every 24 hours
a. How long does it take the Earth rotate through an angle of 315°?
b. How long does it take the Earth rotate through an angle π/6?
3.Find the measure of an angle between 0° and 360° coterminal with each given angle.Draw the angles.
a. 385°
b. 575°
c. -405°
d. 7π/3
Click here to see answer by ikleyn(53427)

Question 1165687: Line Quadrant
y = −x
II
sin θ =

cos θ =

tan θ =

csc θ =

sec θ =

cot θ =

Click here to see answer by CPhill(2138)

Question 1165712: For the function f(x) = tan x, show that f(x+y)
- f(x)= sec^2 x tan y/1-tan x tan y
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Question 733683: Dermont and tony are competing to see whose house is the tallest. Early in the afternoon, tony, who is 4 feet tall, measured his shadow to be 9.6 inches and the shadow of his house to be 62.4 inches. Later in the day, dermont, who is five feet all, measured his shadow to be 15.6 inches and the shadow of his house to be 62.4 inches. Who lives in the taller house?
Click here to see answer by ikleyn(53427)

Question 733671: 1)Find all real numbers that satisfy the equation: cos x = square root 3 / 2.
2)Solve the equation: 6 cos(Alpha)+3=0 for 0degree 3)Find all real numbers in the interval[0,2pi) that satisfy the equation: cos^2x+2cosx+1=0.
4)Find all values of x in the interval [0degree,360 degree)that satisfy the equation. Round approximate answer to the nearest tenth of a degree: sin^2x+8sinx-4=0.
5)Find all angles in degrees that satisfy the equation: cos alpha=-0.609
Click here to see answer by ikleyn(53427)

Question 1166568: At 12noon,a ship steaming steadily due east at 10knots, observed a light house at a bearing 060° and half an hour later the same light house is observed at a bearing of 040° . calculate the time to the nearest minutes at which the bearing will be 020° and the distance from the ship to the light house at this time.[take 1knots=1nautical mile per hour].

Click here to see answer by CPhill(2138)

Question 734985: what is the period of y=2sin(2x)+cos(3x)
Click here to see answer by ikleyn(53427)

Question 734965: what is the exact value of cos 450
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Question 1210455: Skyball is a popular sport in the Magical Realm where the Chaser of each team is tasked with catching the Silver Orb. In today’s match, Lina and Kai are the Chasers for opposing teams. Kai is floating directly above Lina when both spot the Silver Orb. In this instance, Lina’s angle of elevation to the Orb is 35°, while Kai’s angle of depression to it is 42°. Meanwhile, Orin, seated 8.2 meters directly below the Orb, watches Lina with a 28° angle of elevation. (Show your illustration)
(a) What is the distance between Lina and the Silver Orb? How about between Kai and the Orb?
(b) Orin wants Kai’s team to win, so he magically lifts the Silver Orb 1.5 meters higher. How far is Kai from the Orb now?
Click here to see answer by KMST(5330)

Question 736643: What is the simplified form of sin(x + pi)?
a. cos x b. sin x c. -sin x d. -cos x

Click here to see answer by ikleyn(53427)

Question 742212: I need to find the sum of the following infinite series: ∑[n-0,∞,1/4^n]
(The n-0 is below the ∑, and the ∞ is above. The 1/4^n is one the right side of the ∑)
Thanks!
Click here to see answer by ikleyn(53427)

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(53427)

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(53427)

Question 578708: find the angle(s) that would make each statement true.
theta equals arc csc (sqrt of 2)
Click here to see answer by ikleyn(53427)

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(53427)

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(53427)

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(53427)

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(53427)

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(53427)

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(53427)

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(53427)

Question 1179653: https://gyazo.com/848645a235363970dae8196a58a2bbdc
Click here to see answer by ikleyn(53427)

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(53427)

Question 1121000: Solve the system:
Click here to see answer by mccravyedwin(417)

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(20077)

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(13258)

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(53427)

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(3828)

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(53427)

Question 1210238: -5pi/8 radians
Find a coterminal angle between 0 and 2pm for each given angle
Click here to see answer by greenestamps(13258)

Question 1210238: -5pi/8 radians
Find a coterminal angle between 0 and 2pm for each given angle
Click here to see answer by ikleyn(53427)

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(2138)

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(2138)

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(2138)

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(53427)

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(2138)

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(2138)

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(2138)

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(2138)

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