5TT Without using a calculator, compute the sine and cosine of 6 What is the reference angle? In what quadrant is this angle? sin (5) = 5πT COS = 6 (Type sqrt(2) for √2 and sqrt(3) for √3.) by using the reference angle. radians. (answer 1, 2, 3, or 4)
5TT Without using a calculator, compute the sine and cosine of 6 What is the reference angle? In what quadrant is this angle? sin (5) = 5πT COS = 6 (Type sqrt(2) for √2 and sqrt(3) for √3.) by using the reference angle. radians. (answer 1, 2, 3, or 4)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter2: Right Triangle Trigonometry
Section: Chapter Questions
Problem 6GP
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Question
![### Calculating the Sine and Cosine of \( \frac{5\pi}{6} \) Using the Reference Angle
Without using a calculator, compute the sine and cosine of \( \frac{5\pi}{6} \) by using the reference angle.
#### Step-by-Step Guide:
1. **Determine the Reference Angle:**
\[
\text{What is the reference angle?} \ \underline{\hspace{2cm}} \ \text{radians.}
\]
2. **Identify the Quadrant:**
\[
\text{In what quadrant is this angle?} \ \underline{\hspace{2cm}} \ \text{(answer 1, 2, 3, or 4)}
\]
3. **Compute the Sine Value:**
\[
\sin\left(\frac{5\pi}{6}\right) = \underline{\hspace{3cm}}
\]
4. **Compute the Cosine Value:**
\[
\cos\left(\frac{5\pi}{6}\right) = \underline{\hspace{3cm}}
\]
**Note:** Use \( \text{sqrt(2)} \) for \( \sqrt{2} \) and \( \text{sqrt(3)} \) for \( \sqrt{3} \).
By understanding the reference angle and the quadrant, we can determine the trigonometric values based on known values from the unit circle. The reference angle is the angle formed with the x-axis, which helps us to find the corresponding sine and cosine values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc94e4e1c-3d4e-4486-b985-b30353acec86%2F3ed861c0-1f8f-4839-8f4a-f26baae00da9%2F6y5pkda_processed.png&w=3840&q=75)
Transcribed Image Text:### Calculating the Sine and Cosine of \( \frac{5\pi}{6} \) Using the Reference Angle
Without using a calculator, compute the sine and cosine of \( \frac{5\pi}{6} \) by using the reference angle.
#### Step-by-Step Guide:
1. **Determine the Reference Angle:**
\[
\text{What is the reference angle?} \ \underline{\hspace{2cm}} \ \text{radians.}
\]
2. **Identify the Quadrant:**
\[
\text{In what quadrant is this angle?} \ \underline{\hspace{2cm}} \ \text{(answer 1, 2, 3, or 4)}
\]
3. **Compute the Sine Value:**
\[
\sin\left(\frac{5\pi}{6}\right) = \underline{\hspace{3cm}}
\]
4. **Compute the Cosine Value:**
\[
\cos\left(\frac{5\pi}{6}\right) = \underline{\hspace{3cm}}
\]
**Note:** Use \( \text{sqrt(2)} \) for \( \sqrt{2} \) and \( \text{sqrt(3)} \) for \( \sqrt{3} \).
By understanding the reference angle and the quadrant, we can determine the trigonometric values based on known values from the unit circle. The reference angle is the angle formed with the x-axis, which helps us to find the corresponding sine and cosine values.
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