### Trigonometric Functions of Right Triangles#### Goal:Find the exact values of the six trigonometric functions for the angle \( \theta \) in each of the two given right triangles.#### Diagrams:1. **Smaller Triangle** (with side lengths): - Hypotenuse: Not given explicitly. - Opposite side to \( \theta \): 1 - Adjacent side to \( \theta \): 2 ``` 2 ________ | / | / | / | / | / |θ/ 1 |/ ```2. **Larger Triangle** (with side lengths): - Hypotenuse: Not given explicitly. - Opposite side to \( \theta \): 3 - Adjacent side to \( \theta \): 6 ``` 6 ________ | / | / | / | / | / |θ/ 3 |/ ```#### Trigonometric Functions for Right Triangles:For a right triangle with an angle \( \theta \):- Opposite: The side opposite to \( \theta \).- Adjacent: The side adjacent to \( \theta \).- Hypotenuse: The side opposite the right angle (the longest side).The six trigonometric functions are defined as:1. **Sine** (\(\sin \theta\)) = Opposite / Hypotenuse2. **Cosine** (\(\cos \theta\)) = Adjacent / Hypotenuse3. **Tangent** (\(\tan \theta\)) = Opposite / Adjacent4. **Cosecant** (\(\csc \theta\)) = Hypotenuse / Opposite5. **Secant** (\(\sec \theta\)) = Hypotenuse / Adjacent6. **Cotangent** (\(\cot \theta\)) = Adjacent / Opposite#### Calculation Fields:To calculate the trigonometric functions for each triangle:##### Smaller Triangle:- \(\sin \theta = \)- \(\cos \theta = \)- \(\tan \theta = \)- \(\csc \theta = \)- \(\sec \theta = \)- \(\cot \theta

Find the exact values of the six trigonometric functions of the angle 0 for each of the two triangles. 2 1 Smaller triangle sin 8 = cos 8 = tan 8 = csc 8= sec 8= cot 8 = 0 6 0 3 Larger triangle sin 0 = cos 8= tan 8 = csc 8= sec 8= cot 8 =

Find the exact values of the six trigonometric functions of the angle 0 for each of the two triangles. 2 1 Smaller triangle sin 8 = cos 8 = tan 8 = csc 8= sec 8= cot 8 = 0 6 0 3 Larger triangle sin 0 = cos 8= tan 8 = csc 8= sec 8= cot 8 =

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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### Trigonometric Functions of Right Triangles

#### Goal:
Find the exact values of the six trigonometric functions for the angle \( \theta \) in each of the two given right triangles.

#### Diagrams:
1. **Smaller Triangle** (with side lengths):
- Hypotenuse: Not given explicitly.
- Opposite side to \( \theta \): 1
- Adjacent side to \( \theta \): 2

```
2
________
| /
| /
| /
| /
| /
|θ/ 1
|/
```

2. **Larger Triangle** (with side lengths):
- Hypotenuse: Not given explicitly.
- Opposite side to \( \theta \): 3
- Adjacent side to \( \theta \): 6

```
6
________
| /
| /
| /
| /
| /
|θ/ 3
|/
```

#### Trigonometric Functions for Right Triangles:
For a right triangle with an angle \( \theta \):
- Opposite: The side opposite to \( \theta \).
- Adjacent: The side adjacent to \( \theta \).
- Hypotenuse: The side opposite the right angle (the longest side).

The six trigonometric functions are defined as:
1. **Sine** (\(\sin \theta\)) = Opposite / Hypotenuse
2. **Cosine** (\(\cos \theta\)) = Adjacent / Hypotenuse
3. **Tangent** (\(\tan \theta\)) = Opposite / Adjacent
4. **Cosecant** (\(\csc \theta\)) = Hypotenuse / Opposite
5. **Secant** (\(\sec \theta\)) = Hypotenuse / Adjacent
6. **Cotangent** (\(\cot \theta\)) = Adjacent / Opposite

#### Calculation Fields:
To calculate the trigonometric functions for each triangle:

##### Smaller Triangle:
- \(\sin \theta = \)
- \(\cos \theta = \)
- \(\tan \theta = \)
- \(\csc \theta = \)
- \(\sec \theta = \)
- \(\cot \theta

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