Question

use a calculator to estimate the value of the following. round to the nearest ten - thousandth.
$sin 86.4^{circ}$

Explanation:

Step1: Set calculator to degree mode

Ensure the calculator is in degree mode (not radians) to calculate the sine of an angle in degrees.

Step2: Calculate sin(86.4°)

Using a calculator, input \( \sin(86.4^\circ) \). The calculator gives approximately 0.9975640503.

Step3: Round to ten - thousandth

The ten - thousandth place is the fourth decimal place. The number is 0.9975640503. The digit in the fifth decimal place is 6, which is greater than or equal to 5, so we round up the fourth decimal place. So 0.9975640503 rounded to the nearest ten - thousandth is 0.9976.

Answer:

\( 0.9976 \)