Trigonometry Answers

If sinA =3/5
and sinB =5/13
. Where A and B are acute angles. Find (cosAcosB+sinAsinB)

63/65
43/56
3/5
2/5

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed the angle of depression to the boat is 16°18'. When the boat stops, the angle of depression is 48°51'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

if secA = x+1/4x , prove that secA +tanA= 2x or 1/2x?

If 4sin^2x=1,where 0<x<360 , how many values does x take?

Round answer to two significant digits.

House B is located at a bearing of N67°E from house A. House C is 495 meters from house A at a bearing of S68°E. House B is located at a bearing of N11°W from house C. Find the distance from house A to house B

Round your answer to two significant digits.

A plane leaves airport A and travels 640 miles to airport B at a bearing of N32°E. The plane leaves airport B and travels to airport C 310 miles away at a bearing of S72°E. Find the distance from airport A to airport C

what is the x-intercept of f(x)=2/5-3?

Model equation for tide: h=2 cos⁡(π/6 t-2π/3)+4
Given the above, a large boat needs at least 4 meters of water to secure it at the end of the pier. Determine what span of time after noon, including both a starting and ending time, the boat can first safely be secured, justifying your answer.
So far, I have gotten this, but I'm stuck!
4=2 cos⁡(π/6 t-2π/3)+4
0=2 cos⁡(π/6 t-2π/3)
0=cos⁡(π/6 t-2π/3)
0=cos⁡(π/6 t) cos⁡(2π/3)+sin⁡(π/6 t) sin⁡(2π/3)

Am I even remotely on the right track??? Can someone PLEASE help?!?

Prove that in a triangle with angles A, B and C; and sides of length a, b and c that:

1/[(a-b)(a-c)]*tan(A/2) + 1/[(b-c)(b-a)]*tan(B/2) + 1/[(c-b)(c-a)]*tan(C/2) =(Area of triangle)^(-1)

{NOTE: 'a' is the length of side opposite to angle A, likewise 'b' is the length of side opposite to angle B and similarly 'c' is the length of side opposite to angle C.}

• How can a trigonometric function be chosen to model periodic phenomena with specified amplitude, frequency, and midline?