Given sin θ = 3/5 and cos θ > 0, compute tan θ.

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Multiple Choice

Given sin θ = 3/5 and cos θ > 0, compute tan θ.

Explanation:
Tangent is the ratio of sine to cosine. With sin θ = 3/5, use sin^2 + cos^2 = 1 to find cos θ. sin^2 θ = 9/25, so cos^2 θ = 1 − 9/25 = 16/25, giving cos θ = ±4/5. Since cos θ > 0, take cos θ = 4/5. Then tan θ = sin θ / cos θ = (3/5) / (4/5) = 3/4. The positive value aligns with the given cos > 0, and the other numbers would correspond to sin or to reciprocals that don’t match tan with the provided sine. So tan θ = 3/4.

Tangent is the ratio of sine to cosine. With sin θ = 3/5, use sin^2 + cos^2 = 1 to find cos θ. sin^2 θ = 9/25, so cos^2 θ = 1 − 9/25 = 16/25, giving cos θ = ±4/5. Since cos θ > 0, take cos θ = 4/5. Then tan θ = sin θ / cos θ = (3/5) / (4/5) = 3/4. The positive value aligns with the given cos > 0, and the other numbers would correspond to sin or to reciprocals that don’t match tan with the provided sine. So tan θ = 3/4.

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