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Ch. 2 - Acute Angles and Right Triangles
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook
All textbooksLial 12th EditionCh. 2 - Acute Angles and Right TrianglesProblem 2.3.32
Chapter 3, Problem 2.3.32

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2.
sin θ = 0.84802194

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1
Identify the given equation: \(\sin \theta = 0.84802194\) and the interval for \(\theta\) is \([0^\circ, 90^\circ)\).
Recall that the sine function is positive and increasing in the interval \([0^\circ, 90^\circ)\), so there will be exactly one solution in this range.
Use the inverse sine function (arcsin) to find \(\theta\): \(\theta = \arcsin(0.84802194)\).
Make sure your calculator is set to degree mode before calculating \(\arcsin(0.84802194)\) to get the angle in degrees.
Calculate the value of \(\theta\) and round it to six decimal places as required.

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Key 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 in the range [-1, 1], arcsin(y) returns an angle θ in the interval [-90°, 90°]. This is essential for determining θ when sin θ is known.
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Inverse Sine

Domain and Range of Sine Function

The sine function outputs values between -1 and 1 for all real angles. When solving for θ in [0°, 90°), the sine function is positive and increasing, ensuring a unique solution for sin θ = 0.84802194 within this interval.
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Domain and Range of Function Transformations

Decimal Degree Precision

Angles can be expressed in degrees with decimal precision for accuracy. Here, the solution requires θ to be given to six decimal places, which means careful use of a calculator or software to obtain and report the angle with high precision.
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Converting between Degrees & Radians
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