QQuestionMathematics
QuestionMathematics
The terminal side of angle θ intersects the unit circle in the first quadrant at (13 / 15,y). What are the values of sinθ and cosθ?
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Answer
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Step 1
y = \sqrt{1 - \frac{169}{225}} = \sqrt{\frac{56}{225}} = \frac{\sqrt{56}}{15}
First, we find the value of the y-coordinate for the point (13 / 15, y) on the unit circle: Since the point is in the first quadrant, the y-coordinate will be positive. We can use the Pythagorean theorem to find the value of y: Simplify the expression inside the square root:
Step 2
cos(\theta) = \frac{13}{15} \approx 0.8660
Now, we can find the values of sinθ and cosθ using the definitions of sine and cosine for points on the unit circle:
Final Answer
sin(\theta) = \frac{\sqrt{56}}{15} \approx 0.4364 cos(\theta) = \frac{13}{15} \approx 0.8660
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