ms. nazer
geo - b - 9.4 -9.5 - trigonometric functions worksheet
in exercises 3-8, find sin d, sin e, cos d, and cos e. write each answer as a
fraction and as a decimal rounded to four places.
3.
4.
5.
6.
7.
8.
in exercises 9-12, write the expression in terms of
cosine. (see example 2.)
9. $sin 37^{circ}$
10. $sin 81^{circ}$
11. $sin 29^{circ}$
12. $sin 64^{circ}$
in exercises 13-16, write the expression in terms of
sine.
13. $cos 59^{circ}$
14. $cos 42^{circ}$
15. $cos 73^{circ}$
16. $cos 18^{circ}$

Question

Accepted Answer

### Exercises 3-8
# Explanation:
For each right triangle, use the trigonometric ratios:
$\sin(	heta) = \frac{	ext{opposite side}}{	ext{hypotenuse}}$, $\cos(	heta) = \frac{	ext{adjacent side}}{	ext{hypotenuse}}$

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#### Problem 3
## Step1: Identify sides for ∠D
Opposite to ∠D: 12, Hypotenuse: 15, Adjacent to ∠D: 9
$\sin D = \frac{12}{15} = \frac{4}{5} = 0.8000$
$\cos D = \frac{9}{15} = \frac{3}{5} = 0.6000$
## Step2: Identify sides for ∠E
Opposite to ∠E: 9, Hypotenuse:15, Adjacent to ∠E:12
$\sin E = \frac{9}{15} = \frac{3}{5} = 0.6000$
$\cos E = \frac{12}{15} = \frac{4}{5} = 0.8000$
# Answer:
$\sin D = \frac{4}{5} = 0.8000$, $\cos D = \frac{3}{5} = 0.6000$
$\sin E = \frac{3}{5} = 0.6000$, $\cos E = \frac{4}{5} = 0.8000$

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#### Problem 4
## Step1: Identify sides for ∠D
Opposite to ∠D: 35, Hypotenuse:37, Adjacent to ∠D:12
$\sin D = \frac{35}{37} \approx 0.9459$
$\cos D = \frac{12}{37} \approx 0.3243$
## Step2: Identify sides for ∠E
Opposite to ∠E:12, Hypotenuse:37, Adjacent to ∠E:35
$\sin E = \frac{12}{37} \approx 0.3243$
$\cos E = \frac{35}{37} \approx 0.9459$
# Answer:
$\sin D = \frac{35}{37} \approx 0.9459$, $\cos D = \frac{12}{37} \approx 0.3243$
$\sin E = \frac{12}{37} \approx 0.3243$, $\cos E = \frac{35}{37} \approx 0.9459$

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#### Problem 5
## Step1: Identify sides for ∠D
Opposite to ∠D:28, Hypotenuse:53, Adjacent to ∠D:45
$\sin D = \frac{28}{53} \approx 0.5283$
$\cos D = \frac{45}{53} \approx 0.8491$
## Step2: Identify sides for ∠E
Opposite to ∠E:45, Hypotenuse:53, Adjacent to ∠E:28
$\sin E = \frac{45}{53} \approx 0.8491$
$\cos E = \frac{28}{53} \approx 0.5283$
# Answer:
$\sin D = \frac{28}{53} \approx 0.5283$, $\cos D = \frac{45}{53} \approx 0.8491$
$\sin E = \frac{45}{53} \approx 0.8491$, $\cos E = \frac{28}{53} \approx 0.5283$

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#### Problem 6
## Step1: Identify sides for ∠D
Opposite to ∠D:36, Hypotenuse:45, Adjacent to ∠D:27
$\sin D = \frac{36}{45} = \frac{4}{5} = 0.8000$
$\cos D = \frac{27}{45} = \frac{3}{5} = 0.6000$
## Step2: Identify sides for ∠E
Opposite to ∠E:27, Hypotenuse:45, Adjacent to ∠E:36
$\sin E = \frac{27}{45} = \frac{3}{5} = 0.6000$
$\cos E = \frac{36}{45} = \frac{4}{5} = 0.8000$
# Answer:
$\sin D = \frac{4}{5} = 0.8000$, $\cos D = \frac{3}{5} = 0.6000$
$\sin E = \frac{3}{5} = 0.6000$, $\cos E = \frac{4}{5} = 0.8000$

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#### Problem 7
## Step1: Identify sides for ∠D
Opposite to ∠D:$13\sqrt{3}$, Hypotenuse:26, Adjacent to ∠D:13
$\sin D = \frac{13\sqrt{3}}{26} = \frac{\sqrt{3}}{2} \approx 0.8660$
$\cos D = \frac{13}{26} = \frac{1}{2} = 0.5000$
## Step2: Identify sides for ∠E
Opposite to ∠E:13, Hypotenuse:26, Adjacent to ∠E:$13\sqrt{3}$
$\sin E = \frac{13}{26} = \frac{1}{2} = 0.5000$
$\cos E = \frac{13\sqrt{3}}{26} = \frac{\sqrt{3}}{2} \approx 0.8660$
# Answer:
$\sin D = \frac{\sqrt{3}}{2} \approx 0.8660$, $\cos D = \frac{1}{2} = 0.5000$
$\sin E = \frac{1}{2} = 0.5000$, $\cos E = \frac{\sqrt{3}}{2} \approx 0.8660$

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#### Problem 8
## Step1: Identify sides for ∠D
Opposite to ∠D:8, Hypotenuse:17, Adjacent to ∠D:15
$\sin D = \frac{8}{17} \approx 0.4706$
$\cos D = \frac{15}{17} \approx 0.8824$
## Step2: Identify sides for ∠E
Opposite to ∠E:15, Hypotenuse:17, Adjacent to ∠E:8
$\sin E = \frac{15}{17} \approx 0.8824$
$\cos E = \frac{8}{17} \approx 0.4706$
# Answer:
$\sin D = \frac{8}{17} \approx 0.4706$, $\cos D = \frac{15}{17} \approx 0.8824$
$\sin E = \frac{15}{17} \approx 0.8824$, $\cos E = \frac{8}{17} \approx 0.4706$

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### Exercises 9-12 (Rewrite sine as cosine)
Use co-function identity: $\sin(	heta) = \cos(90^\circ - 	heta)$
# Explanation:
Apply co-function identity to each angle.
## Step1: Solve problem 9
$\sin37^\circ = \cos(90^\circ-37^\circ)$
## Step2: Solve problem 10
$\sin81^\circ = \cos(90^\circ-81^\circ)$
## Step3: Solve problem 11
$\sin29^\circ = \cos(90^\circ-29^\circ)$
## Step4: Solve problem 12
$\sin64^\circ = \cos(90^\circ-64^\circ)$
# Answer:
9. $\cos53^\circ$
10. $\cos9^\circ$
11. $\cos61^\circ$
12. $\cos26^\circ$

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### Exercises 13-16 (Rewrite cosine as sine)
Use co-function identity: $\cos(	heta) = \sin(90^\circ - 	heta)$
# Explanation:
Apply co-function identity to each angle.
## Step1: Solve problem 13
$\cos59^\circ = \sin(90^\circ-59^\circ)$
## Step2: Solve problem 14
$\cos42^\circ = \sin(90^\circ-42^\circ)$
## Step3: Solve problem 15
$\cos73^\circ = \sin(90^\circ-73^\circ)$
## Step4: Solve problem 16
$\cos18^\circ = \sin(90^\circ-18^\circ)$
# Answer:
13. $\sin31^\circ$
14. $\sin48^\circ$
15. $\sin17^\circ$
16. $\sin72^\circ$

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QUESTION IMAGE

Question

Explanation:

Exercises 3-8

Problem 3

Step1: Identify sides for ∠D

Step2: Identify sides for ∠E

Step1: Solve problem 9

Step2: Solve problem 10

Step3: Solve problem 11

Step4: Solve problem 12

Step1: Solve problem 13

Step2: Solve problem 14

Step3: Solve problem 15

Step4: Solve problem 16

Answer:

Problem 4

Step1: Identify sides for ∠D

Step2: Identify sides for ∠E