Textbook Question
Find each exact function value. See Example 2.
cos 7π/4
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3. Unit Circle
Trigonometric Functions on the Unit Circle
Problem 33
Textbook Question
Find a calculator approximation to four decimal places for each circular function value. See Example 3. sin 0.6109
Verified step by step guidance1
Identify the circular function to evaluate, which is \(\sin(0.6109)\), where the angle is given in radians.
Recall that the sine function, \(\sin(\theta)\), gives the y-coordinate of the point on the unit circle corresponding to the angle \(\theta\) measured in radians.
Use a scientific calculator or a calculator tool that can compute sine values for angles in radians. Make sure the calculator is set to radian mode, not degree mode.
Input the value 0.6109 into the calculator and apply the sine function to get the approximate value.
Round the result to four decimal places to obtain the final approximation for \(\sin(0.6109)\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Understanding Circular Functions
Circular functions, such as sine, cosine, and tangent, relate an angle to ratios of sides in a right triangle or coordinates on the unit circle. The sine function gives the y-coordinate of a point on the unit circle corresponding to a given angle measured in radians.
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Radian Measure
Angles in trigonometry are often measured in radians, where one radian is the angle subtended by an arc equal in length to the radius of the circle. Understanding that 0.6109 is in radians is essential for correctly evaluating the sine function using a calculator.
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Using a Calculator for Trigonometric Values
Calculators can approximate trigonometric function values to a desired decimal precision. It is important to ensure the calculator is set to the correct mode (radians or degrees) before computing sin(0.6109), and then round the result to four decimal places as required.
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