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 trig - ratio definitions

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, the opposite side to the angle is 6 and the adjacent side is 23.

Step2: Determine the trig - ratio

Using the tangent ratio, $\tan\theta=\frac{6}{23}\approx0.26$. To find the angle $\theta$, we use the inverse - tangent function, $\theta = \tan^{-1}(\frac{6}{23})\approx\tan^{-1}(0.26)$.

Answer:

None of the given options are correct. The correct inverse - trigonometric function to use is $\tan^{-1}(0.26)$.