25. In which quadrant would the terminal ray of an angle lie if it had a positive tangent and a negative sine ? *

Trigonometry (MindTap Course List)
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Author:Charles P. McKeague, Mark D. Turner
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Chapter2: Right Triangle Trigonometry
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Problem 1RP: The origins of the sine function are found in the tables of chords for a circle constructed by the...
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**Question 25: Determining the Quadrant of an Angle**

Question: 
In which quadrant would the terminal ray of an angle lie if it had a positive tangent and a negative sine?

Explanation: 
In the unit circle, the tangent of an angle is positive in both the first and third quadrants. However, the sine of an angle is positive in the first and second quadrants. Since we need an angle with a positive tangent and a negative sine, we analyze both conditions together. The only quadrant where both conditions are true (positive tangent and negative sine) is the third quadrant.

Answer: 
The terminal ray of the angle would lie in the third quadrant.
Transcribed Image Text:**Question 25: Determining the Quadrant of an Angle** Question: In which quadrant would the terminal ray of an angle lie if it had a positive tangent and a negative sine? Explanation: In the unit circle, the tangent of an angle is positive in both the first and third quadrants. However, the sine of an angle is positive in the first and second quadrants. Since we need an angle with a positive tangent and a negative sine, we analyze both conditions together. The only quadrant where both conditions are true (positive tangent and negative sine) is the third quadrant. Answer: The terminal ray of the angle would lie in the third quadrant.
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