CPM Homework Help : PC3 Problem 10-132

Evaluate each of the following trigonometric expressions. Use exact values.

Hint:

Angle Sum Identities
$\left. \begin{array} { c } { \operatorname { sin } ( A + B ) = \operatorname { sin } ( A ) \operatorname { cos } ( B ) + \operatorname { cos } ( A ) \operatorname { sin } ( B ) } \\ { \operatorname { cos } ( A + B ) = \operatorname { cos } ( A ) \operatorname { cos } ( B ) - \operatorname { sin } ( A ) \operatorname { sin } ( B ) } \\ { \operatorname { tan } ( A + B ) = \frac { \operatorname { tan } ( A ) + \operatorname { tan } ( B ) } { 1 - \operatorname { tan } ( A ) \operatorname { tan } ( B ) } } \end{array} \right.$

Angle Differences Identities
$\left. \begin{array} { c } { \operatorname { sin } ( A - B ) = \operatorname { sin } ( A ) \operatorname { cos } ( B ) - \operatorname { cos } ( A ) \operatorname { sin } ( B ) } \\ { \operatorname { cos } ( A - B ) = \operatorname { cos } ( A ) \operatorname { cos } ( B ) - \operatorname { cos } ( A ) \operatorname { sin } ( B ) } \\ { \operatorname { tan } ( A - B ) = \frac { \operatorname { tan } ( A ) - \operatorname { tan } ( B ) } { 1 + \operatorname { tan } ( A ) \operatorname { tan } ( B ) } } \end{array} \right.$

Half-Angel Identities for Sine and Cosine
$\operatorname { sin } ( \frac { \theta } { 2 } ) = \pm \sqrt { \frac { 1 - \operatorname { cos } ( \theta ) } { 2 } } \quad \operatorname { cos } ( \frac { \theta } { 2 } ) = \pm \sqrt { \frac { 1 + \operatorname { cos } \theta } { 2 } }$

$\sin( \frac { 7 \pi } { 8 } )$
Hint (a):
$\frac{7\pi}{8} = \frac{7\pi/4}{2}$

$\cos(105º)$
Hint (b):
$105º = 210º/2$ or $105º = 45º + 60º$