Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.

sin s = 0.9918

검증된 단계별 안내

Identify the problem: We need to find the value of \( s \) in the interval \( [0, \frac{\pi}{2}] \) such that \( \sin s = 0.9918 \).

Recall that to find an angle \( s \) given \( \sin s = a \), we use the inverse sine function (also called arcsine), denoted as \( \sin^{-1} \) or \( \arcsin \). So, \( s = \arcsin(0.9918) \).

Make sure the value \( 0.9918 \) is within the valid range for sine, which is \( [-1, 1] \). Since it is, the inverse sine function is defined.

Calculate \( s = \arcsin(0.9918) \) using a calculator set to radians mode to get the angle in radians.

Round the result to four decimal places to get the approximate value of \( s \) within the interval \( [0, \frac{\pi}{2}] \).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Sine Function and Its Range

The sine function relates an angle in a right triangle to the ratio of the opposite side over the hypotenuse. Its values range between -1 and 1, and within the interval [0, π/2], sine values increase from 0 to 1. Understanding this helps identify valid solutions for the equation sin s = 0.9918.

Inverse Sine Function (Arcsin)

The inverse sine function, denoted as arcsin or sin⁻¹, returns the angle whose sine is a given value. It is used to find the angle s when sin s is known. Since arcsin outputs values in [-π/2, π/2], restricting the domain to [0, π/2] ensures a unique solution for s.

Radian Measure and Interval Constraints

Angles in trigonometry are often measured in radians, where π radians equal 180 degrees. The interval [0, π/2] corresponds to angles from 0 to 90 degrees, representing the first quadrant where sine values are positive and increasing. This constraint limits the solution to a specific range.

Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.sin s = 0.9918