Use reference angles to evaluate the following expressions. For the angle 2, the reference angle is sin(2) = ? ? sin( sin() = For the angle, the reference angle is cos=0 cos(7) = ? cos( 6 For the angle 3π 4' tan(3r) = ? tan( the reference angle is So, So, So,
Use reference angles to evaluate the following expressions. For the angle 2, the reference angle is sin(2) = ? ? sin( sin() = For the angle, the reference angle is cos=0 cos(7) = ? cos( 6 For the angle 3π 4' tan(3r) = ? tan( the reference angle is So, So, So,
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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Question
![### Using Reference Angles to Evaluate Trigonometric Expressions
To evaluate trigonometric functions using reference angles, follow the steps outlined below for each given angle. Identify the reference angle and use it to determine the value of the trigonometric function.
#### Steps:
1. **Determine the Reference Angle:**
- The reference angle is the smallest angle between the terminal side of the given angle and the x-axis.
2. **Evaluate the Trigonometric Function:**
- Use the reference angle to find the trigonometric function value. Adjust for the sign based on the quadrant where the original angle lies.
---
#### Example Problems:
1. **For the Angle \( \frac{2\pi}{3} \):**
- **Reference Angle Calculation:**
\[
\text{The reference angle is } \boxed{\phantom{}}
\]
- **Sine Function Evaluation:**
\[
\sin \left( \frac{2\pi}{3} \right) = \boxed{\phantom{?}} \sin \left( \boxed{\phantom{}} \right) = \boxed{\phantom{}}
\]
2. **For the Angle \( \frac{7\pi}{6} \):**
- **Reference Angle Calculation:**
\[
\text{The reference angle is } \boxed{\phantom{}}
\]
- **Cosine Function Evaluation:**
\[
\cos \left( \frac{7\pi}{6} \right) = \boxed{\phantom{?}} \cos \left( \boxed{\phantom{}} \right) = \boxed{\phantom{}}
\]
3. **For the Angle \( \frac{3\pi}{4} \):**
- **Reference Angle Calculation:**
\[
\text{The reference angle is } \boxed{\phantom{}}
\]
- **Tangent Function Evaluation:**
\[
\tan \left( \frac{3\pi}{4} \right) = \boxed{\phantom{?}} \tan \left( \boxed{\phantom{}} \right) = \boxed{\phantom{}}
\]
Refer to the steps and examples above to solve each trigonometric expression using the reference angles. Notice how you can generalize this method for a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e08cb41-5b2e-4118-8784-a24243109431%2F183b4984-48df-42bc-80ae-5c9373ba9d17%2Fl233b0n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Using Reference Angles to Evaluate Trigonometric Expressions
To evaluate trigonometric functions using reference angles, follow the steps outlined below for each given angle. Identify the reference angle and use it to determine the value of the trigonometric function.
#### Steps:
1. **Determine the Reference Angle:**
- The reference angle is the smallest angle between the terminal side of the given angle and the x-axis.
2. **Evaluate the Trigonometric Function:**
- Use the reference angle to find the trigonometric function value. Adjust for the sign based on the quadrant where the original angle lies.
---
#### Example Problems:
1. **For the Angle \( \frac{2\pi}{3} \):**
- **Reference Angle Calculation:**
\[
\text{The reference angle is } \boxed{\phantom{}}
\]
- **Sine Function Evaluation:**
\[
\sin \left( \frac{2\pi}{3} \right) = \boxed{\phantom{?}} \sin \left( \boxed{\phantom{}} \right) = \boxed{\phantom{}}
\]
2. **For the Angle \( \frac{7\pi}{6} \):**
- **Reference Angle Calculation:**
\[
\text{The reference angle is } \boxed{\phantom{}}
\]
- **Cosine Function Evaluation:**
\[
\cos \left( \frac{7\pi}{6} \right) = \boxed{\phantom{?}} \cos \left( \boxed{\phantom{}} \right) = \boxed{\phantom{}}
\]
3. **For the Angle \( \frac{3\pi}{4} \):**
- **Reference Angle Calculation:**
\[
\text{The reference angle is } \boxed{\phantom{}}
\]
- **Tangent Function Evaluation:**
\[
\tan \left( \frac{3\pi}{4} \right) = \boxed{\phantom{?}} \tan \left( \boxed{\phantom{}} \right) = \boxed{\phantom{}}
\]
Refer to the steps and examples above to solve each trigonometric expression using the reference angles. Notice how you can generalize this method for a
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