can you help me with trigonometric equations?

Question

cos θ=-sin(-θ)

solve each equation on the interval 0≤θ<2Π

Answer 1

 

cos^2 = sin^2

 

Since:

cos^2 = 1-sin^2

 

1 - sin^2 = sin^2

 

Add sin^2 to both sides:

 

1 = 2 sin^2

 

Divide by 2:

 

1/2 = sin^2

 

Take the square root:

 

+/- sqrt(2)/2 =  sin (-x)

 

Where is sine +sqrt(2)/2?   pi/4  and 3pi/4

 

Sine is -sqrt(2)/2 at 5pi/4 and 7pi/4.

 

Since,

 

cos(pi/4) = -sin(-pi/4)  

 

cos(5pi/4) = -sin(-5pi/4)

 

 

θ = { pi/4, 5pi/4 }

 

Answer 2

cosθ = -sin(-θ) is equivalent to

tanθ = 1, since sine is an odd function.

Answer: θ = pi/4, 5pi/4