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Answer to Problem 2AYU
Solution:
True.Trigonometric identity in the form sin�(-θ )+cos�(-θ)= cos�θ-sin�θ exists.
Explanation of Solution
:
Given:
Trigonometric identity is in the form of sin�(-θ )+cos�(-θ)= cos�θ-sin�θ
Calculation:
Consider a unit circle.
Equation of a unit circle = x2+ y2 =1. -------1
If P (x, y) is a point on the unit circle that corresponds to angle θ then
y = sin θ, x = cos θ. ------2
Using the symmetry, the point Q on the unit circle corresponds to the angle (-θ).
The point Q has the coordinates (x, -y).
Using values from equation 2 to obtain the coordinates of Q
Q(x, -y) = Q (cos θ, -sin θ). ---3
By definition of trigonometric function
Coordinate of Q is formed as
sin�(-θ)= -y
cos�(-θ)= x
Using the coordinates of Q from
Equation3
sin�(-θ )+cos�(-θ)=
-sin�(θ )+cos�θ
Rearranging
sin�(-θ )+cos�(-θ)= cos�θ- sin�θ
Chapter 7 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Calculus and Its Applications (11th Edition)
University Calculus: Early Transcendentals (4th Edition)
Glencoe Math Accelerated, Student Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
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