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. (3 , ―4)
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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 25
The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 147° 12' , 30° 19'
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 and minutes into a consistent format if needed, keeping degrees and minutes separate for easier calculation: \(147^\circ 12'\) and \(30^\circ 19'\).
Add the degrees parts of the two given angles: \(147^\circ + 30^\circ\) and add the minutes parts: \(12' + 19'\).
If the sum of the minutes is 60 or more, convert the excess minutes into degrees (since \$60'$ equals \(1^\circ\)) and add that to the degrees sum.
Subtract the total sum of the two given angles from \(180^\circ\) to find the measure of the third angle, keeping track of degrees and minutes separately.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Triangle Angle Sum Property
The sum of the interior angles of any triangle is always 180 degrees. This fundamental property allows us to find the measure of the third angle when the other two angles are known by subtracting their sum from 180 degrees.
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Sum and Difference of Tangent
Conversion Between Degrees and Minutes
Angles can be expressed in degrees (°) and minutes ('). One degree equals 60 minutes. When performing addition or subtraction with angles, it is important to correctly convert and carry over between degrees and minutes to maintain accuracy.
Recommended video:
5:04Converting between Degrees & Radians
Subtraction of Angles with Degrees and Minutes
To find the unknown angle, subtract the sum of the given angles from 180°. This requires careful subtraction of degrees and minutes, borrowing 1 degree as 60 minutes if necessary, similar to subtraction in time calculations.
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3:18Adding and Subtracting Complex Numbers
Related Practice
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. (0, ―3)
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Textbook Question
Concept Check What is wrong with the following item that appears on a trigonometry test? "Find sec θ , given that cos θ = 3/2 . "
Textbook Question
Find the measure of each marked angle. See Example 2.
Textbook Question
Find the measure of each marked angle. See Example 2.
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Textbook Question
Find the six trigonometric function values for each angle. Rationalize denominators when applicable.
4
views