Question

identify the correct inverse trigonometric function to use to solve for the given angle.
?
6
23
o a. tan^(-1)(3.83)
o b. sin^(-1)(3.83)
o c. cos^(-1)(.26)
o d. sin^(-1)(.26)

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For the given angle, the opposite side has length 23 and the adjacent side has length 6.

Step2: Calculate the tangent of the angle

$\tan\theta=\frac{23}{6}\approx3.83$. To find the angle $\theta$, we use the inverse - tangent function, $\theta = \tan^{-1}(\frac{23}{6})=\tan^{-1}(3.83)$.

Answer:

A. $\tan^{-1}(3.83)$