Question

in exercises 9-12, write the expression in terms of cosine. (see example 2.)

1. $sin 37^circ$
2. $sin 81^circ$
3. $sin 29^circ$
4. $sin 64^circ$

in exercises 13-16, write the expression in terms of sine.

1. $cos 59^circ$
2. $cos 42^circ$
3. $cos 73^circ$
4. $cos 18^circ$

$cos 37=$

Explanation:

Step1: Use co-function identity

Recall the co-function identity: $\sin\theta = \cos(90^\circ - \theta)$

Step2: Solve Exercises 9-12

For Exercise 9:

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

For Exercise 10:

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

For Exercise 11:

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

For Exercise 12:

Substitute $\theta=64^\circ$:
$\sin64^\circ = \cos(90^\circ - 64^\circ) = \cos26^\circ$

Step3: Use co-function identity

Recall the co-function identity: $\cos\theta = \sin(90^\circ - \theta)$

Step4: Solve Exercises 13-16

For Exercise 13:

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

For Exercise 14:

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

For Exercise 15:

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

For Exercise 16:

Substitute $\theta=18^\circ$:
$\cos18^\circ = \sin(90^\circ - 18^\circ) = \sin72^\circ$

Answer:

1. $\cos53^\circ$
2. $\cos9^\circ$
3. $\cos61^\circ$
4. $\cos26^\circ$
5. $\sin31^\circ$
6. $\sin48^\circ$
7. $\sin17^\circ$
8. $\sin72^\circ$