Textbook Question
Use a calculator to approximate each value in decimal degrees.
θ = arccos (-0.39876459)
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5. Inverse Trigonometric Functions and Basic Trigonometric Equations
Inverse Sine, Cosine, & Tangent
Problem 59
Textbook Question
Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)
y = arcsin 0.92837781
Verified step by step guidance1
Understand that the function \( y = \arcsin(x) \) gives the angle \( y \) whose sine is \( x \). Here, you need to find \( y \) such that \( \sin(y) = 0.92837781 \).
Make sure your calculator is set to radian mode, as the problem specifies. This ensures the output angle \( y \) will be in radians, not degrees.
Input the value \( 0.92837781 \) into the inverse sine function on your calculator, often labeled as \( \sin^{-1} \) or \( \arcsin \).
The calculator will return an approximate value for \( y \) in radians, which is the angle whose sine is \( 0.92837781 \).
Interpret the result as the principal value of \( y = \arcsin(0.92837781) \), which lies within the range \( [-\frac{\pi}{2}, \frac{\pi}{2}] \).
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Inverse Trigonometric Functions
Inverse trigonometric functions, like arcsin, return the angle whose sine is a given number. For example, arcsin(0.92837781) gives the angle y such that sin(y) = 0.92837781. These functions are essential for finding angles from known ratios.
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Radian Mode in Calculators
Calculators can measure angles in degrees or radians. Radian mode means angles are measured in radians, the standard unit in higher mathematics. Ensuring the calculator is in radian mode is crucial for correct results when working with trigonometric functions in calculus or advanced math.
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Domain and Range of arcsin Function
The arcsin function is defined for inputs between -1 and 1, and its output (range) is limited to angles between -π/2 and π/2 radians. Understanding this helps interpret the result correctly and ensures the input value is valid for the function.
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