Final answer:
To find sin(θ) given cos(θ) = 7/9 in the first quadrant, use the Pythagorean identity. Calculate sin^2(θ) = 1 - cos^2(θ) and take the positive square root. The answer is sin(θ) = 4/9.
Step-by-step explanation:
The student has asked to find sin(θ) given that cos(θ) = 7/9 and θ is in the first quadrant. We can use the Pythagorean identity, which states that sin^2(θ) + cos^2(θ) = 1. Since we know cos(θ), we can rearrange this to solve for sin(θ).
Firstly, we square the known cosine value: cos^2(θ) = (7/9)^2 = 49/81. Next, we use the Pythagorean identity to find sin^2(θ): sin^2(θ) = 1 - cos^2(θ) = 1 - 49/81 = 32/81.
As θ is in the first quadrant where all trigonometric functions are positive, we take the positive square root to find sin(θ): sin(θ) = sqrt(32/81) = 4/9. Therefore, sin(θ) = 4/9.