Given sin θ = -3/5 and csc θ = -5/3 in quadrant III, find the value of other trigonometric functions using a Pythagorean Identit

Question

3 years ago

14

y. Show your work.
Part I: Find the value of cos θ and sec θ

Part II: Using your answers from Part I, find the value of tan θ

2 answers:

mixas84 [53] · Answer 1 · 2021-11-06T12:53:54+03:00

8 0

Iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiuuuuu

Mariana [72] · Answer 2 · 2021-11-06T10:59:59+03:00

6 0

I. Since $\theta$ lies in quadrant 3, we know $\cos\theta$ . The Pythagorean identity tells us

$\cos^2\theta+\sin^2\theta=1\implies\cos\theta=-\sqrt{1-\sin^2\theta}=\boxed{-\dfrac45}$

$\implies\sec\theta=\dfrac1{\cos\theta}=\boxed{-\dfrac54}$

II. By definition of tangent,

$\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{-\frac35}{-\frac45}=\boxed{\dfrac34}$