Find and solve the exact value of each of the following under the given conditions tan alpha = -frac{7}{24}, alpha lies in quadrant 2, cos beta = frac{3}{4}, beta lies in quadrant 1 a. sin(alpha + beta) b. cos(alpha + beta) c. tan (alpha + beta)

Lewis Harvey 2020-11-11 Answered
Find and solve the exact value of each of the following under the given conditions tan α= 724, α lies in quadrant 2,
cos β=34, β lies in quadrant 1
a. sin(α + β)
b. cos(α + β)
c. tan(α + β)
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Expert Answer

hesgidiauE
Answered 2020-11-12 Author has 106 answers

Given:
tan α= 724, α lies in quadrant 2
cos β=34, β lies in quadrant 1
Thus, using trigonometric ratio
sin α=725
cos α= 2425
sin β=74
tan β=sqrt73
a) sin(α + β)=sin α cos β + cos α sin β
=(725 × 34) + (2425 × 74)
=21100  247100
sin(α + β)=21  247100
b) cos(α + β)=cos α cos β  sin α sin β
=(2425 × 34)  (725 × 74)
= 72100  77100
cos(α + β)=72  77100
c) tan(α + β)=tan α + tan β1  tan α tan β
=724 + 731  (724)(73)
=7 + 87241 + 7772
=21 + 24772 + 77
Multiply and divide by conjugate of denominator,
tan(α + β)=21 + 24772 + 77 × 72  7772  77
tan(α + β)=2688 + 187574841

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Jeffrey Jordon
Answered 2021-11-03 Author has 2047 answers

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