Answer:
(c) 0.923
Step-by-step explanation:
The coordinates of a point on the unit circle are (cos(θ), sin(θ)). That is, the y-coordinate of a point on the terminal ray will have the same sign as the sine of the angle. Here, the sign of the sine is positive, eliminating the first two answer choices.
We know that cos(θ) < sin(θ) for reference angles greater than 45°, where both values are √2/2 ≈ 0.707. Since 5 < 12, that means the angle of interest here will have a sine that is more than 0.707. Only one of the positive answer choices is in this range: sin(θ) ≈ 0.923.
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Additional comment
The value of sin(θ) is precisely ...
sin(θ) = y/√(x²+y²) = 12/√(25+144) = 12/13
sin(θ) = 0.923076...(6-digit repeat)
