Question

value: 2
identify the correct inverse trigonometric function to use to solve for the given angle.
48
?
34
a. tan⁻¹(.71)
b. sin⁻¹(.71)
c. cos⁻¹(1.41)
d. sin⁻¹(1.41)

Explanation:

Step1: Recall trigonometric ratio definitions

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For the given angle, the opposite side has length 34 and the adjacent side has length 48.

Step2: Calculate the tangent value

$\tan\theta=\frac{34}{48}\approx0.71$. To find the angle $\theta$, we use the inverse - tangent function, $\theta = \tan^{-1}(\frac{34}{48})=\tan^{-1}(0.71)$. Also, note that the range of the sine and cosine functions is $[- 1,1]$, and options c and d have values outside this range for the inverse - sine and inverse - cosine operations which is not possible.

Answer:

A. $\tan^{-1}(.71)$