Textbook Question
In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.
tan 32.7°
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1. Measuring Angles
Angles in Standard Position
1:52 minutesProblem 1.2.55
Textbook Question
In Exercises 55–58, use a calculator to find the value of the acute angle θ to the nearest degree. sin θ = 0.2974
Verified step by step guidance1
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.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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Inverse Sine
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.
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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.
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