Question

1.)The angle θ lies in Quadrant IV. sinθ=−2/3 What is cosθ?

Answer 1

Answer:

1. From sin²θ +cos²θ =1 and sinθ=-2/3, we see that cosθ=√(1-sin²θ) or cosθ=√5/3, where the sign of cosine is positive as it is in Quadrant IV. x lies in 4th quadrant , cos x is +ve. , cos x = √5/3. Answer.

answer : cos x = √5/3

2.  4/3

3.  sin (- theta)  = - sin (x)        so sin x = 1/6

 tan = sin / cos   =  1/6  /  cos  =  - sqrt35/35     solve for cos

                        cos =  1/6 * (-35/sqrt35)

                       

                                  = -35 sqrt35 /210

answer : −35/√210

4. The cosine function is an even function, so cos(θ) = cos(-θ).

The relationship between sin(θ) and cos(θ) is sin(θ) = ±√(1 -cos(θ)^2)

For sin(θ) < 0 and cos(θ) = (√3)/4,  sin(θ) = -√(1 -3/16) = -√(13/16)

sin(θ) = -(√13)/4   For sin(θ) < 0 and cos(0) = √(3/4), ...

sin(θ) = -√(1 -3/4) = -√(1/4)       sin(θ) = -1/2

answer : -13/√4

5.  answer : tan^2 θ ⋅ cos^2 θ = 1 − cos^2 θ would be the first step