Final answer:
To find the value of cos θ when sin θ = 7/25, substitute the given value of sin θ into the Pythagorean identity sin^2 θ + cos^2 θ = 1 and solve for cos θ. The value of cos θ is 24/25.
Step-by-step explanation:
To find the value of cos θ when sin θ = 7/25, we can use the Pythagorean identity sin^2 θ + cos^2 θ = 1.
Given sin θ = 7/25, we can substitute this value in the equation and solve for cos θ:
sin^2 θ + cos^2 θ = 1
(7/25)^2 + cos^2 θ = 1
49/625 + cos^2 θ = 1
cos^2 θ = 1 - 49/625
cos^2 θ = 625/625 - 49/625
cos^2 θ = 576/625
cos θ = ± √(576/625)
cos θ = ± 24/25
Therefore, the value of cos θ is a. 24/25.