PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Question
Chapter 5.4, Problem 43E
To determine
To find: the exact value of the trigonometric expression when
Expert Solution & Answer
Answer to Problem 43E
Explanation of Solution
Given information:
Given expression,
Calculation:
Consider that
The sine of an angle is equal to opposite side over the hypotenuse. Since
Since cosine of an angle is equal to adjacent side over the hypotenuse and
Therefore:
Since,
Since the side of an angle is equal to opposite side over the hypotenuse. Therefore:
Apply the sum formula for sine that is:
Substitute:
And,
So,
Therefore,
Chapter 5 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Prob. 59ECh. 5.1 - Prob. 60ECh. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.1 - Prob. 63ECh. 5.1 - 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- A factorization A = PDP 1 is not unique. For A= 7 2 -4 1 1 1 5 0 2 1 one factorization is P = D= and P-1 30 = Use this information with D₁ = to find a matrix P₁ such that - -1 -2 0 3 1 - - 1 05 A-P,D,P P1 (Type an integer or simplified fraction for each matrix element.)arrow_forwardMatrix A is factored in the form PDP 1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 30 -1 - 1 0 -1 400 0 0 1 A= 3 4 3 0 1 3 040 3 1 3 0 0 4 1 0 0 003 -1 0 -1 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) A basis for the corresponding eigenspace is { A. There is one distinct eigenvalue, λ = B. In ascending order, the two distinct eigenvalues are λ₁ ... = and 2 = Bases for the corresponding eigenspaces are { and ( ), respectively. C. In ascending order, the three distinct eigenvalues are λ₁ = = 12/2 = and 3 = Bases for the corresponding eigenspaces are {}, }, and { respectively.arrow_forwardN Page 0.6. 0.4. 0.2- -0.2- -0.4- -6.6 -5 W 10arrow_forward
- Diagonalize the following matrix, if possible. 8 0 6 - 8 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 8 0 OA. For P= D= 0 3 6 0 B. For P = D= 0 -6 8 0 C. For P = D= 0 - 8 D. The matrix cannot be diagonalized.arrow_forwardCalculus lll May I please have the solutions for the following exercises? Thank youarrow_forwardCalculus lll May I please have the solution for the following question? Thank youarrow_forward
- Find three horizontal tangents between [0,10]arrow_forward4 In the integral dxf1dy (7)², make the change of variables x = ½(r− s), y = ½(r + s), and evaluate the integral. Hint: Find the limits on r and s by sketching the area of integration in the (x, y) plane along with the r and s axes, and then show that the same area can be covered by s from 0 to r and r from 0 to 1.arrow_forward7. What are all values of 0, for 0≤0<2л, where 2 sin² 0=-sin? - 5π 6 π (A) 0, л, and 6 7π (B) 0,л, 11π , and 6 6 π 3π π (C) 5π 2 2 3 , and π 3π 2π (D) 2' 2'3 , and 3 4元 3 1 די } I -2m 3 1 -3 บ 1 # 1 I 3# 3m 8. The graph of g is shown above. Which of the following is an expression for g(x)? (A) 1+ tan(x) (B) 1-tan (x) (C) 1-tan (2x) (D) 1-tan + X - 9. The function j is given by j(x)=2(sin x)(cos x)-cos x. Solve j(x) = 0 for values of x in the interval Quiz A: Topic 3.10 Trigonometric Equations and Inequalities Created by Bryan Passwaterarrow_forward
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