QuestionAdvanced Functions (MHF4U)
6. Use compound angles to evaluate the exact value for the following. (a) $\sin \frac{\pi}{12}$
6(a) $\qquad$ (b) $\cos \frac{17 \pi}{12}$
6(b) $\qquad$ (c) $\tan \left(-\frac{5 \pi}{12}\right)$
6(c) $\qquad$
7. Simplify and then evaluate each expression (no decimals). (a) $\cos \left(\frac{7 \pi}{12}\right) \cos \left(\frac{5 \pi}{12}\right)+\sin \left(\frac{7 \pi}{12}\right) \sin \left(\frac{5 \pi}{12}\right)$
7(a) simplified: $\qquad$ evaluate: $\qquad$ (b) $\sin 2 x \cos x-\cos 2 x \sin x$, let: $x=\frac{4 \pi}{3}$
7(b) simplified: $\qquad$ evaluate: $\qquad$ (c) $2 \sin \frac{\pi}{8} \cos \frac{\pi}{8}$
7(b) simplified: $\qquad$ evaluate: $\qquad$
8. Express as a single trigonometric ratio (a) $\cos ^{2}\left(\frac{\beta}{4}\right)-\sin ^{2}\left(\frac{\beta}{4}\right)$
8(a) $\qquad$ (b) $1-2 \sin ^{2} 3 x$
8(b) $\qquad$
9. Find the exact value of $\frac{\tan \frac{\pi}{10}+\tan \frac{\pi}{15}}{1-\tan \frac{\pi}{10} \tan \frac{\pi}{15}}$.
9. $\qquad$
10. Angles $A$ and $B$ are located in the first quadrant. If $\sin A=\frac{5}{13}$
10. $\qquad$ and $\cos B=\frac{3}{5}$, determine the exact value of $\cos (A+B)$.
11. Given $\sqrt{3} \cos \theta-2 \cos \theta \sin \theta=0$, determine the exact angles of rotation
11. $\qquad$ $\qquad$ $\qquad$ $\qquad$
12. A child swings on a playground swing set. If the length of the
12. $\qquad$ swing is 3 m and the child swings through an angle of $\frac{\pi}{9}$, determine the exact are length through which the child travels.