Question

use the given information to find the exact value of a. sin 2θ, b. cos 2θ, and c. tan 2θ.
cosθ = 24/26, θ lies in quadrant iv
a. sin 2θ = -120/169 (type an integer or a fraction. simplify your answer.)
b. cos 2θ = 119/169 (type an integer or a fraction. simplify your answer.)
c. tan 2θ = (type an integer or a fraction. simplify your answer.)

Explanation:

Step1: Recall the formula for \(\tan2\theta\)

The formula for \(\tan2\theta=\frac{\sin2\theta}{\cos2\theta}\)

Step2: Substitute the values of \(\sin2\theta\) and \(\cos2\theta\)

We know that \(\sin2\theta =-\frac{120}{169}\) and \(\cos2\theta=\frac{119}{169}\)

So, \(\tan2\theta=\frac{-\frac{120}{169}}{\frac{119}{169}}\)

Step3: Simplify the expression

When we divide \(-\frac{120}{169}\) by \(\frac{119}{169}\), the \(169\) in the numerator and denominator cancels out.

We get \(\tan2\theta =-\frac{120}{119}\)

Answer:

\(-\frac{120}{119}\)