Explanation Definition used: Definition of the trigonometric functions : “Let ( x , y ) be any point on the terminal side of the angle θ in standard position, and let r be the distance between the origin and the given point, then the six trigonometry functions are defined as sin θ = y r , cos θ = x r , tan θ = y x , csc θ = r y , sec θ = r x and cot θ = x y ”. Theorem used: Pythagorean theorem: “If c is the length of the hypotenuse and a and b are the length of the other two sides, the Pythagorean theorem is c 2 = a 2 + b 2 ”. Calculation: The given trigonometric function is cos θ = 3 8 . By the trigonometric definition of cos θ = x r , the value of x = 3 and r = 8 . Consider the values x = 3 and r = 8 and use the Pythagorean Theorem to find the value of y as follows. y = r 2 − x 2 = 8 2 − ( 3 ) 2 = 64 − 9 = 55 The current situation can be represents as shown below in Figure 1

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Chapter 4, Problem 24RE

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The approximate values of sinθ and tanθ by using the given value cosθ=38.

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Chapter 4, Problem 23RE

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1. Matrix Operations Given: A = [ 33 ]A-[3-321] -3 B = [342]B-[3-41-2] (a) A² A2 Multiply A× A: -3 = (3 x 32x-3) (3 x 22 x 1) | = |[19–63 |-9-3 -6+21] = A² = 33 33 1-3×3+1x-3) (-3×2+1x1) [12]A2=[3-321][3-321]=[(3×3+2x-3)(-3×3+1x-3)(3×2+2×1)(-3×2+1×1)]=[9-6-9-36+2-6+1 ]=[3-128-5] (b) | A ||A| Determinant of A | A | (3 × 1) (2 x-3)=3+ 6 = 9|A|=(3×1)-(2x-3)=3+6=9 (c) Adjoint of A Swap diagonal elements and change sign of off-diagonals: A = [33], so adj (A) = |¯²]A=[3-321], so adj(A)=[13–23] -3 (d) B-¹B-1 First find | B ||B|: |B | (3x-2)- (1 × -4) = -6 + 4 = −2|B|=(3x-2)-(1x-4)=-6+4=-2 Then the adjoint of B: adj (B) = [² 3 adj(B)=[-24-13] Now, B-1 1 = |B| · adj (B) = 1 [²¯¯³¹³] = [2₂ B 0.5 |B-1=|B|1-adj(B)=-21[-24-13]=[1-20.5-1.5] 2. (a) Matrix Method: Solve (2x + 3y = 6 (2x-3y=14 {2x+3y=62x-3y=14 Matrix form: 22 33-22 = [223-3][xy]=[614] Find inverse of coefficient matrix: Determinant: | M | (2x-3) - (3 x 2) = -6 -6 = -12|M|=(2x-3)-(3×2)=-6-6=-12 Adjoint: adj(M) = [3]adj(M)-[-3-2-32] So…

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Chapter 4 Solutions

Basic Technical Mathematics

Ch. 4.1 - Change 17°24′ to decimal form. Ch. 4.1 - Prob. 2PE Ch. 4.1 - Prob. 3PE Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E

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The approximate values of sin θ and tan θ by using the given value cos θ = 3 8 .

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