Textbook Question
Find the values of the six trigonometric functions for an angle in standard position having each given point on its terminal side. Rationalize denominators when applicable. (―8 , 15)
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Ch. 1 - Trigonometric Functions
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 2, Problem 30
The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2.
17° 41' 13" , 96° 12' 10"
Verified step by step guidance1
Recall that the sum of the interior angles of any triangle is always \(180^\circ\).
Convert the given angles from degrees, minutes, and seconds into a consistent format to make addition easier. Remember that 1 degree = 60 minutes and 1 minute = 60 seconds.
Add the two given angles together by separately adding degrees, minutes, and seconds. If the seconds sum to 60 or more, convert the excess into minutes. Similarly, if the minutes sum to 60 or more, convert the excess into degrees.
Subtract the sum of the two given angles from \(180^\circ\) to find the measure of the third angle. Perform this subtraction carefully, borrowing minutes or seconds if necessary.
Express the result in degrees, minutes, and seconds format to give the measure of the third angle.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angle Measurement in Degrees, Minutes, and Seconds
Angles can be expressed in degrees (°), minutes ('), and seconds ("). One degree equals 60 minutes, and one minute equals 60 seconds. Understanding this notation is essential for accurately adding or subtracting angles given in this format.
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Reference Angles on the Unit Circle
Sum of Angles in a Triangle
The sum of the interior angles in any triangle is always 180 degrees. This fundamental property allows us to find the unknown angle when the other two angles are known by subtracting their sum from 180°.
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4:47Sum and Difference of Tangent
Conversion and Subtraction of Angles
When subtracting angles expressed in degrees, minutes, and seconds, it may be necessary to convert between these units to perform the calculation correctly. Borrowing from degrees to minutes or minutes to seconds ensures accurate subtraction.
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3:18Adding and Subtracting Complex Numbers
Related Practice
Textbook Question
Determine the signs of the trigonometric functions of an angle in standard position with the given measure. See Example 2. 84°
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Textbook Question
Find the values of the six trigonometric functions for an angle in standard position having each given point on its terminal side. Rationalize denominators when applicable. (6√3 , ―6)
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Textbook Question
Find the measure of each marked angle. See Example 2 supplementary angles with measures 6𝓍 - 4 and 8𝓍 - 12 degrees
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Textbook Question
Sketch an angle θ in standard position such that θ has the least positive measure, and the given point is on the terminal side of θ. Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. See Examples 1, 2, and 4. (―2√3 , 2)
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Textbook Question
Find the measure of each marked angle. See Example 2 supplementary angles with measures 10𝓍 + 7 and 7𝓍 + 3 degrees