What is sqrt(25-(5sin(θ))^2) ?

The solution to sqrt(25-(5sin(θ))^2) is 5sqrt(cos^2(θ))

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simplify sqrt(25-(5sin(θ))^2)

simplify

25 - (5 sin (θ))^{2}

5 cos^{2} (θ)

Solution steps

25 - (5 sin (θ))^{2}

Apply exponent rule:

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

= 25 - 5^{2} sin^{2} (θ)

Factor

25 - 5^{2} sin^{2} (θ) : 25 (1 - sin^{2} (θ))

= 25 (1 - sin^{2} (θ))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 25 - sin^{2} (θ) + 1

25 = 5

= 5 - sin^{2} (θ) + 1

Rewrite using trig identities

= 5 cos^{2} (θ)

sin (π t + π)

- cos (4 x - 7 x)

sin (t + \frac{π}{6})

cos (π t + π)

csc (- cot (x))

What is sqrt(25-(5sin(θ))^2) ?
The solution to sqrt(25-(5sin(θ))^2) is 5sqrt(cos^2(θ))