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In Exercises 59–62, use a calculator to find the value of the acute angle θ in radians, rounded to three decimal places. cos θ = 0.4112
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Blitzer 3rd EditionCh. 1 - Angles and the Trigonometric FunctionsProblema 1.2.55
Blitzer 3rd EditionCh. 1 - Angles and the Trigonometric FunctionsProblema 1.2.55Capitolo 1, Problema 1.2.55
In Exercises 55–58, use a calculator to find the value of the acute angle θ to the nearest degree. sin θ = 0.2974
Guida verificata passo dopo passo1
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.
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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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Percorso guidato
4:03
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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Percorso guidato
4:22Domain and Range of Function Transformations
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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Percorso guidato
4:45How to Use a Calculator for Trig Functions
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