Answer to Question #139916 in Trigonometry for Michael

Question

4. Use the appropriate compound angle formula to determine the exact value of each expression

a) sin ( pi + Pi over 6 )
b) tan ( Pi over 4 + Pi )
c) cos ( -Pi - pi over 4 )

Answer 1

a) sin($\pi$ )cos($\pi$/6) + cos($\pi$ )sin($\pi$/6) = 0 + (-1)(1/2) = -1/2

b) tan($\pi$/4 + $\pi$) = (tan($\pi$ /4) + tan($\pi$)) / (1-tan($\pi$/4)tan($\pi$)) = (1 + 0)/(1-0) = 1

c) cos (-)($\pi$ +$\pi$/4) = cos($\pi$+ $\pi$ /4) = cos($\pi$ )cos($\pi$/4) - sin($\pi$)sin($\pi$/4) = (-1)(1/ $\sqrt{2}$ ) + 0 = -1/$\sqrt{2}$