Consider the following right triangle: 11 7 Give the exact values of the following in the blanks below: Blank 1: sin(0) Blank 2: sec(0) Blank 3: tan(e)

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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Consider the following right triangle:

```
       ___
     |        \
     |          \
     |            \
  |     θ           \
    |__|_________\ 
        7                         11
```

Give the **exact** values of the following in the blanks below:

- **Blank 1: sin(θ)**
- **Blank 2: sec(θ)**
- **Blank 3: tan(θ)**

To solve, use the properties of the right triangle:

1. Identify the side lengths: the opposite side to θ is 7, and the hypotenuse is 11.
2. Use the Pythagorean theorem to find the adjacent side: \( \text{adj} = \sqrt{11^2 - 7^2} = \sqrt{121 - 49} = \sqrt{72} = 6\sqrt{2} \).

Now calculate the trigonometric functions:
- **sin(θ) = opposite/hypotenuse = 7/11**
- **sec(θ) = hypotenuse/adjacent = 11/(6√2) = 11√2/12**
- **tan(θ) = opposite/adjacent = 7/(6√2) = 7√2/12**
Transcribed Image Text:Consider the following right triangle: ``` ___ | \ | \ | \ | θ \ |__|_________\ 7 11 ``` Give the **exact** values of the following in the blanks below: - **Blank 1: sin(θ)** - **Blank 2: sec(θ)** - **Blank 3: tan(θ)** To solve, use the properties of the right triangle: 1. Identify the side lengths: the opposite side to θ is 7, and the hypotenuse is 11. 2. Use the Pythagorean theorem to find the adjacent side: \( \text{adj} = \sqrt{11^2 - 7^2} = \sqrt{121 - 49} = \sqrt{72} = 6\sqrt{2} \). Now calculate the trigonometric functions: - **sin(θ) = opposite/hypotenuse = 7/11** - **sec(θ) = hypotenuse/adjacent = 11/(6√2) = 11√2/12** - **tan(θ) = opposite/adjacent = 7/(6√2) = 7√2/12**
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