High School

If [tex]\sin \theta = \frac{13}{15}[/tex], then find [tex]\cos \theta[/tex].

(Note: The first correct answer will be marked as "Brainliest.")

Answer :

Final answer:

To find the cosine of θ when the sine of θ is equal to 13/15, substitute sinθ into the Pythagorean identity sin^2θ + cos^2θ = 1 and solve for cosθ.

Explanation:

To find the cosine of θ when the sine of θ is equal to 13/15, we can use the Pythagorean identity: sin^2θ + cos^2θ = 1. Since sinθ = 13/15, we can substitute it into the equation: (13/15)^2 + cos^2θ = 1. Solving for cosθ, we get cosθ = sqrt(1 - (13/15)^2).

Using a calculator, we can find that cosθ ≈ 12/15 = 4/5.

Learn more about Finding cosine given sine here:

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