Final answer:
To find sin θ given sec θ = 4, use the reciprocal identity of secant to get cos θ and then apply the Pythagorean identity to calculate sin θ as √(15/16), assuming θ is in the first quadrant.
Step-by-step explanation:
If sec θ = 4, we can find sin θ by using trigonometric identities.
The secant function is the reciprocal of cosine, which means that sec θ = 1/cos θ.
Therefore, if sec θ = 4, then cos θ = 1/4. To find the sine value, we can use the Pythagorean identity sin2 θ + cos2 θ = 1.
Substituting the value of cosine we have, sin2 θ = 1 - (1/4)2. Sin2 θ becomes 1 - 1/16, which simplifies to 15/16.
Taking the square root to find sin θ, we ensure we consider the correct sign based on the angle quadrant.
Assuming angle θ is in the first quadrant, where sine is positive, we get sin θ = √(15/16).