Question

If $\sin\theta = \frac{2}{5}$, $\theta$ in quadrant II, find the exact value of (a) $\cos\theta$ (b) $\sin\left(\theta + \frac{\pi}{6}\right)$ (c) $\cos\left(\theta - \frac{\pi}{3}\right)$ (d) $\tan\left(\theta + \frac{\pi}{4}\right)$

          If $\sin\theta = \frac{2}{5}$, $\theta$ in quadrant II, find the exact value of
(a) $\cos\theta$
(b) $\sin\left(\theta + \frac{\pi}{6}\right)$
(c) $\cos\left(\theta - \frac{\pi}{3}\right)$
(d) $\tan\left(\theta + \frac{\pi}{4}\right)$

If sinθ = (2)/(5), θ in quadrant II, find the exact value of
(a) cosθ
(b) sin(θ + (π)/(6))
(c) cos(θ - (π)/(3))
(d) tan(θ + (π)/(4))

Added by Rachel A.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Darshan Maheshwari

11/03/2021

Step 1

We can use the Pythagorean identity to find the value of cos\theta: cos^2\theta = 1 - sin^2\theta cos^2\theta = 1 - (2/5)^2 cos^2\theta = 1 - 4/25 cos^2\theta = 21/25 cos\theta = ±√(21/25) Since \theta is in quadrant II, where cosine is negative, we Show more…

Show all steps

Thanks for your feedback!

If sin heta =(2)/(5), heta in quadrant II, find the exact value of (a) cos heta (b) sin( heta +(pi )/(6)) (c) cos( heta -(pi )/(3)) (d) tan( heta +(pi )/(4)) 2 If sin 0= 0 in quadrant II,find the exact value of 5 (c) cos[0 - (d) tan[0+ (a) cos0 (b) sin