What is sqrt(81-81sin^2(θ)) ?

The solution to sqrt(81-81sin^2(θ)) is 9cos(θ)

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simplify sqrt(81-81sin^2(θ))

simplify

81 - 81 sin^{2} (θ)

9 cos (θ)

Solution steps

81 - 81 sin^{2} (θ)

Factor

81 - 81 sin^{2} (θ) : 81 (1 - sin^{2} (θ))

= 81 (1 - sin^{2} (θ))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 81 - sin^{2} (θ) + 1

81 = 9

= 9 - sin^{2} (θ) + 1

Use the Pythagorean identity:

1 = cos^{2} (x) + sin^{2} (x)

1 - sin^{2} (x) = cos^{2} (x)

= 9 cos^{2} (θ)

cos^{2} (θ) = cos (θ)

= 9 cos (θ)

- cos (\frac{π}{2} - θ)

sin (2 x - 2 x)

- 2 sin (- \frac{3}{2} t)

cos (- π n^{0})

cos (n \cdot 2 \cdot π)