Question

Given that cosθ = -0.489 where π<θ<3π/2, find sinθ

Trigonometric Functions
ANSWERED
asked 2021-05-22

Given that \(\cos\theta = -0.489\) where \(\pi<\theta<3\frac{\pi}{2}\), find \(\sin\theta\)

Answers (1)

2021-05-23

Use the Pythagorean identity:

\(\sin^2\theta+\cos^2\theta=1\)

\(\sin^2\theta=1−\cos^2\theta\)

Since \(\theta\) is Quadrant III, then \(\sin\theta<0\) so take the negative root:

\(\sin\theta=−\sqrt{1−\cos2\theta}\)

\(\sin\theta=−\sqrt{1−0.489}^{2}\)

\(\sin\theta\approx−0.872\)

0
 
Best answer

expert advice

Need a better answer?
...