The terminal side of an angle θ in standard position in Quadrant I intersects the unit circle at \( (x,...

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10. The terminal side of an angle θ in standard position in Quadrant I intersects the unit circle at $ (x, \frac{7}{25}) $. What is x?
a. $ \frac{18}{25} $
b. $ \frac{25}{24} $
c. $ \frac{24}{25} $
d. $ \frac{7}{24} $

SnapAndSolve AI · Accepted Answer

To find $ x $, use the equation of the unit circle: $ x^2 + y^2 = 1 $.Given $ y = \frac{7}{25} $, substitute into the equation:$ x^2 + \left(\frac{7}{25}\right)^2 = 1 $$ x^2 + \frac{49}{625} = 1 $$ x^2 = 1 - \frac{49}{625} $$ x^2 = \frac{625}{625} - \frac{49}{625} $$ x^2 = \frac{576}{625} $$ x = \sqrt{\frac{576}{625}} $$ x = \frac{24}{25} $The correct answer is c. $ \frac{24}{25} $.

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The terminal side of an angle θ in standard position in Quadrant I intersects the unit circle at \( (x,...

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