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If sin θ = 3/5 and θ is acute, find cos θ.

Mathematics

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Here are the solutions to the problems:

1. If sin⁡θ=3/5\sin \theta = 3/5 and θ\theta is acute, find cos⁡θ\cos \theta.

  1. Use the Pythagorean identity sin⁡2θ+cos⁡2θ=1\sin^2 \theta + \cos^2 \theta = 1.

    (35)2+cos⁡2θ=1\left(\frac{3}{5}\right)^2 + \cos^2 \theta = 1

  2. Solve for cos⁡2θ\cos^2 \theta.

    925+cos⁡2θ=1\frac{9}{25} + \cos^2 \theta = 1 cos⁡2θ=1−925=1625\cos^2 \theta = 1 - \frac{9}{25} = \frac{16}{25}

  3. Take the square root.

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