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)

Question

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)

hesgidiauE · Accepted Answer

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

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

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)

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Answer & Explanation

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