Trigonometry Answers

An observer on a lighthouse in an island 150 feet height above the sea level saw two vessels moving directly towards the lighthouse. He observed that the angle of depression of the vessels are 39 degrees and 25 degrees. Find the distance between the two vessels, assuming that they are coming from the same side of the tower.

1. A hot air balloon is 115 km due east of a landing field A. and another landing field B is 136 km due north of A. Find the distance and the bearing of the second landing field from the hot air balloon. (Disregard the balloon’s elevation.)

(a) Show that sin(3x) + sin(x) = 4sin(x)cos^2(x)

(b) Find all the angles between 0 and "\\pi" which satisfy the equation sin(3x) + sin(x) = 2(cos^2)(x).

The sides of a triangle are in a ratio of 4:5:6. Solve for the smallest angle

Determine the numerical value of the following expression without the use of a calculator:

log10 (1000100)

100

+

X100

n=1

sin(n) + 1

(􀀀1)n

!

vuut

1Y000

m=1

1

cos(m)2

If t = tan("\\theta" /2), show that sin("\\theta" )=2t/(1-t²) and cos ("\\theta" )=(1-t²)/(1+t²). hence solve the equation cos("\\theta" )-2sin("\\theta" )=2

2n+1 > (n + 2) · sin(n) 

determine cos theta to three decimal places where sin theta=6/square root 61 and theta is an angle in the second quadrant

determine sin theta to three decimal places when tan theta=1/2 and theta is an angle in standard position

Find the largest value of parameter a such that equation 12sin²x * cos²x + (10a - 11)(cos⁴x - sin⁴x) = (2a-1)² has at least one real solution.