In Exercises 55–58, use a calculator to find the value of the acute angle θ to the nearest degree. sin θ = 0.2974

검증된 단계별 안내

Identify that the problem requires finding the acute angle \( \theta \) such that \( \sin \theta = 0.2974 \). Since \( \theta \) is acute, it lies between 0° and 90°.

Recall the inverse sine function (also called arcsine), which allows us to find the angle when the sine value is known: \( \theta = \sin^{-1}(0.2974) \).

Use a calculator set to degree mode to compute \( \sin^{-1}(0.2974) \). This will give the measure of \( \theta \) in degrees.

Round the result from the calculator to the nearest whole degree, as the problem requests the angle to the nearest degree.

Verify that the angle is indeed acute (between 0° and 90°) to confirm the solution is valid for the given problem.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

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

Inverse Sine Function (Arcsin)

The inverse sine function, denoted as arcsin or sin⁻¹, is used to find the angle whose sine value is given. For a value y = sin θ, θ = arcsin(y) returns the angle θ in radians or degrees. This is essential for solving equations like sin θ = 0.2974 to find θ.

Domain and Range of Sine and Arcsin

The sine function outputs values between -1 and 1, so the input to arcsin must lie within this range. The arcsin function returns angles only in the range of -90° to 90° (or -π/2 to π/2 radians), which corresponds to acute and some obtuse angles. Understanding this helps identify the correct angle solution.

Using a Calculator to Find Angles

Calculators have a function to compute arcsin values, usually labeled as sin⁻¹. To find the angle θ from sin θ = 0.2974, input 0.2974 and use the inverse sine function. Ensure the calculator is set to the correct mode (degrees) to get the angle in degrees, as required.