Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section: Chapter Questions
Problem 40CT: To determine the angle of elevation of a star in the sky, you align the star and the top of the...
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![### Determining the Corresponding Ordered Pair on the Unit Circle for an Angle of 600°
To determine the ordered pair \((x, y)\) on the unit circle for an angle of 600°, you need to calculate the equivalent angle within the standard range of 0° to 360°.
An angle of 600° can be simplified by subtracting multiples of 360° (since a full circle is 360°):
\[ 600° - 360° = 240° \]
So, the equivalent angle is 240°.
Using the unit circle, the coordinates for 240° are:
\[ \left(-\frac{1}{2}, -\frac{\sqrt{3}}{2}\right) \]
Here are the given choices in the problem:
- A. \(\left( -\frac{1}{2}, \frac{\sqrt{3}}{2} \right)\)
- B. \(\left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right)\)
- C. \(\left( \frac{1}{2}, -\frac{\sqrt{3}}{2} \right)\)
- D. \(\left( -\frac{1}{2}, -\frac{\sqrt{3}}{2} \right)\)
The correct choice is:
- **D.** \(\left( -\frac{1}{2}, -\frac{\sqrt{3}}{2} \right)\)
This pair represents the cosine and sine values of 240° on the unit circle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9fc99ab-b3a9-4577-a5d7-bccfea12d417%2Fff54082e-d9ba-426b-afc5-5d2828cc7e10%2Fgukthzc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining the Corresponding Ordered Pair on the Unit Circle for an Angle of 600°
To determine the ordered pair \((x, y)\) on the unit circle for an angle of 600°, you need to calculate the equivalent angle within the standard range of 0° to 360°.
An angle of 600° can be simplified by subtracting multiples of 360° (since a full circle is 360°):
\[ 600° - 360° = 240° \]
So, the equivalent angle is 240°.
Using the unit circle, the coordinates for 240° are:
\[ \left(-\frac{1}{2}, -\frac{\sqrt{3}}{2}\right) \]
Here are the given choices in the problem:
- A. \(\left( -\frac{1}{2}, \frac{\sqrt{3}}{2} \right)\)
- B. \(\left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right)\)
- C. \(\left( \frac{1}{2}, -\frac{\sqrt{3}}{2} \right)\)
- D. \(\left( -\frac{1}{2}, -\frac{\sqrt{3}}{2} \right)\)
The correct choice is:
- **D.** \(\left( -\frac{1}{2}, -\frac{\sqrt{3}}{2} \right)\)
This pair represents the cosine and sine values of 240° on the unit circle.
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