What is sqrt(64-(8sin(θ))^2) ?

The solution to sqrt(64-(8sin(θ))^2) is 8sqrt(cos^2(θ))

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simplify sqrt(64-(8sin(θ))^2)

simplify

64 - (8 sin (θ))^{2}

8 cos^{2} (θ)

Solution steps

64 - (8 sin (θ))^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= 64 - 8^{2} sin^{2} (θ)

8^{2} = 64

= 64 - 64 sin^{2} (θ)

Factor

64 - 64 sin^{2} (θ) : 64 (1 - sin^{2} (θ))

= 64 (1 - sin^{2} (θ))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 64 - sin^{2} (θ) + 1

64 = 8

= 8 - sin^{2} (θ) + 1

Rewrite using trig identities

= 8 cos^{2} (θ)

- cos (x - 123 π)

e^{- l n (c o s (x)) + c}

cos (2 π f t + π)

\frac{cos ( x )}{sin ( x )} d x

sin (arctan (\frac{x - 1}{x + 3}))

What is sqrt(64-(8sin(θ))^2) ?
The solution to sqrt(64-(8sin(θ))^2) is 8sqrt(cos^2(θ))