QuestionFind $\theta$ in $[0^{\circ}, 90^{\circ}]$ such that $\sin \theta=0.85134345$ . Round to six decimal places.

Studdy Solution

STEP 1

Assumptions1. We are looking for a value of $\theta$ in the interval $\left[0^{\circ},90^{\circ}\right]$ . . The sine of $\theta$ is given as0.85134345.
3. We are assuming that $\theta$ is an angle in a right triangle, not a circular function.
4. We are using the inverse sine function to find the angle.

STEP 2

We can use the inverse sine function, also known as arcsine, to find the angle $\theta$ . The arcsine function is the inverse of the sine function and can be used to find an angle when the sine of the angle is known.
$\theta = \sin^{-1}(0.85134345)$

STEP 3

Now, we can calculate the value of $\theta$ using a calculator. Make sure your calculator is set to degree mode since we are looking for the angle in degrees.
$\theta \approx \sin^{-1}(0.85134345)$

STEP 4

After calculating, we find that the value of $\theta$ is approximately58.688966 degrees.
$\theta \approx58.688966^{\circ}$ So, the value of $\theta$ that satisfies the given statement is approximately58.688966 degrees.

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