1.)The angle θ lies in Quadrant IV. sinθ=−2/3 What is cosθ? a. −2/3
b. 2/3
c. −5/√3
d.5/√3

2.)The angle θ lies in Quadrant I. cosθ=3/5 What is tanθ?

a.4/3
b.−4/5
c. −4/3
d. 4/5

3.)Given sin(−θ)=−1/6 and tanθ=−35/√35. What is the value of cosθ?

a.−35/√210
b.−35/√6
c.35/√210
d.35/√6

4.)cos(−θ)=3/√4, sinθ<0 What is the value of sinθ?

a.13/√4
b. 13/√16
c. −13/√16
d.−13/√4

5.)Marty is proving that the following trigonometric identity is true: tan^2 θ⋅cos^2 θ=1−cos^2 θ

Which step would be the first line of his proof?

a. tan^2 θ⋅cos^2 θ=tan^2 θ
b. tan^2 θ⋅cos^2 θ=sin^2 θ
c. tan^2 θ⋅cos^2 θ=1−sin^2 θ
d. tan^2 θ=1−cos^2 θ⋅cos^2 θ

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

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.

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step-by-step explanation: