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Trigonometry

Solve the equation for all x 0<x<360

Cos(2x) + ½sin(x) = 0

Trigonometry

1. Prove that ( 1 - cos2 x ) cosec2 x = 1 .

2. Prove that (tan x sin x ) + cos x = sec x .

3. Prove that Tan^4 x + Tan^2 x = sec^4 x - sec^2 x .

4. prove that Cot x + Tan x = sec x cosec x.

5. Prove that (1 + sin x) (1 - sin x) = (sec x - Tan x)2 .

2. Prove that (tan x sin x ) + cos x = sec x .

3. Prove that Tan^4 x + Tan^2 x = sec^4 x - sec^2 x .

4. prove that Cot x + Tan x = sec x cosec x.

5. Prove that (1 + sin x) (1 - sin x) = (sec x - Tan x)2 .

Trigonometry

sin(x)=1/2; -pi/2<x<pi/2; find the x

Trigonometry

Prove that the inequality | cos(x)| ≥ 1 − sin2(x) holds true for all x ∈ R.

Trigonometry

sin 60 cos30 cos60 sin30 sin30 o o o o o

Trigonometry

1. Evaluate the following:

a. Cos 118°

b. Sin 135°

c. Tan 252°

d. Sin (-60°)

e. Tan (-148°)

2. Determine the following ratios:

a. Sin 850°

b. Cos 920°

c. Tan 1040°

a. Cos 118°

b. Sin 135°

c. Tan 252°

d. Sin (-60°)

e. Tan (-148°)

2. Determine the following ratios:

a. Sin 850°

b. Cos 920°

c. Tan 1040°

Trigonometry

In a triangle, suppose A=37∘, a=3, and b=4.

Find B, C, and c.

SHOW ALL WORK TO RECEIVE FULL CREDIT

If there are no solutions, show why and then write NO SOLUTIONS as your final answer.

If there are two solutions, find B1, C1, and c1

and then find B2, C2, and c2

.

Trigonometry

Find all solutions in [0,2π) to the equation

2sin^{2}(A)=cos(A)+1

SHOW ALL WORK

Trigonometry

Suppose sin(A)=3/5 and A is in Q2, and cos(B)=−5/13 and B is in Q3. Find the exact value of cos(A+B).

SHOW ALL WORK

Trigonometry

A ladder AB which is setup with B on the horizontal ground and A against a vertical wall, makes an angle of 71 degrees with the ground. it is prevented from slipping by a tight rope PQ of length 1.68 metres, fixed at P to the foot of the wall and at Q to the ladder, PQ being at right angles to AB. Calculate in centimetres

a) The height AP of the ladder above P

b) The length of the ladder?

a) The height AP of the ladder above P

b) The length of the ladder?