(a) Explanation Given: The value of cos α is 1 2 and the value of sin β is − 1 3 . Formula used: sin α = P e r p e n d i c u l a r H y p o t e n u s e tan α = sin α cos α = P H B H = P e r p e n d i c u l a r B a s e cos ( α + β ) = cos α cos β − sin α sin β Calculation: The value of cos α is given that is the fraction of base and hypotenuse that is given in the case the base is 1 and the hypotenuse is 2, there is need to compute the value of perpendicular also known as y . Compute the value of perpendicular ( y ): y 2 = r 2 − x 2 = ( 2 ) 2 − ( 1 ) 2 = 4 − 1 = 3 y = − 3 So, the value of perpendicular ( y ) is negative, the value of 3 is negative because it lies on the fourth quadrant. Compute the value of sin α : sin α = P H = − 3 2 Compute the value of tan α : tan α = sin α cos α = P H B H = − 3 2 1 2 = − 3 Thus, sin α is − 3 2 and tan α is − 3 . The value of sin β is − 1 3 , which means the perpendicular is –-1 and the hypotenuse is 3, again there in need to compute the baser ( x ) (b) To determine To calculate: The value of the expression sin ( α + β ) . (c) To determine To calculate: The value of the expression tan ( α + β ) .

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ISBN: 9780321837240

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 6.2, Problem 62E

(a)

To determine

To calculate: The value of the expression cos(α+β).

(b)

To determine

To calculate: The value of the expression sin(α+β).

(c)

To determine

To calculate: The value of the expression tan(α+β).

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Chapter 6.2, Problem 61E

Chapter 6.2, Problem 63E

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The value of the expression cos ( α + β ) .

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To calculate: The value of the expression cos(α+β).

To calculate: The value of the expression sin(α+β).

To calculate: The value of the expression tan(α+β).

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