  ### Home > PC > Chapter 9 > Lesson 9.3.3 > Problem9-134

9-134.

These expressions look complicated, but they are not if you know your trigonometric identities. Review the addition/subtraction formulas, double-angle formulas, and half-angle formulas in your Tool Kit. Then express each of the problems below in the form $\sin x$ or $\cos x$.

Look in the index and/or glossary for these formulas. 1. $\sin 50° \cos 20° + \cos 50° \sin 20°$

Use the addition formula for sine.
$\sin \left(50° + 20°\right)$

1. $2 \operatorname { sin } \frac { 2 \pi } { 5 } \operatorname { cos } \frac { 2 \pi } { 5 }$

Use the Double-Angle Formula for the sine.

$\text{sin}\left( 2\left( \frac{2\pi}{5} \right) \right)$

1. $\cos110°\cos50°− \sin110°\sin50°$

Use the sum/difference formula for the cosine. Be careful of your sign.

1. $\operatorname { cos } ^ { 2 } \frac { \pi } { 7 } - \operatorname { sin } ^ { 2 } \frac { \pi } { 7 }$

Use one of the Double-Angle Formulas for the cosine.

1. $\sqrt { \frac { 1 + \operatorname { cos } 20 ^ { \circ } } { 2 } }$

Use the Half-Angle Formula for cosine.

1. $\sqrt { \frac { 1 - \operatorname { cos } 20 ^ { \circ } } { 2 } }$

Use the Half-Angle Formula for sine.