Question

write the expression in terms of cosine. (see example 2.)

1. sin 81°
2. sin 37°
3. sin 29°

write the expression in terms of sine.

1. cos 59°
2. cos 42°
3. cos 73°

Explanation:

Step1: Use co-function identity

Recall $\sin\theta = \cos(90^\circ - \theta)$

Step2: Solve problem 4

$\sin81^\circ = \cos(90^\circ - 81^\circ) = \cos9^\circ$

Step3: Solve problem 5

$\sin37^\circ = \cos(90^\circ - 37^\circ) = \cos53^\circ$

Step4: Solve problem 6

$\sin29^\circ = \cos(90^\circ - 29^\circ) = \cos61^\circ$

Step5: Use co-function identity

Recall $\cos\theta = \sin(90^\circ - \theta)$

Step6: Solve problem 7

$\cos59^\circ = \sin(90^\circ - 59^\circ) = \sin31^\circ$

Step7: Solve problem 8

$\cos42^\circ = \sin(90^\circ - 42^\circ) = \sin48^\circ$

Step8: Solve problem 9

$\cos73^\circ = \sin(90^\circ - 73^\circ) = \sin17^\circ$

Answer:

1. $\cos9^\circ$
2. $\cos53^\circ$
3. $\cos61^\circ$
4. $\sin31^\circ$
5. $\sin48^\circ$
6. $\sin17^\circ$