Final answer:
To find sin(θ1) for an angle in the second quadrant with cos(θ1) = -22/29, we use the Pythagorean identity. Carrying out the calculations, we determine that sin(θ1) = 19/29, as sine is positive in the second quadrant.
Step-by-step explanation:
The student has provided the cosine of an angle (cos(θ1)=-22/29) and wishes to find the sine (sin(θ1)) of that same angle, which is located in the second quadrant. Since the given cosine is negative, which is typical for angles in the second quadrant, we calculate the sine using the Pythagorean identity for trigonometric functions.
The Pythagorean identity is sin^2(θ) + cos^2(θ) = 1. To find sin(θ1), we rearrange the identity to sin^2(θ1) = 1 - cos^2(θ1). Substituting the given cosine value gives us sin^2(θ1) = 1 - (-22/29)^2. Calculating this we get sin^2(θ1) = 1 - (484/841), which simplifies to sin^2(θ1) = 357/841. Taking the positive and negative square root of this value gives us sin(θ1) = ± √(357/841).
Since θ1 is in the second quadrant, where sine is positive, we take the positive square root to find sin(θ1) = √(357/841). Simplifying further, we get sin(θ1) = √(357)/√(841), which is sin(θ1) = 19/29.