What is sqrt(9-(3cos(θ))^2) ?

The solution to sqrt(9-(3cos(θ))^2) is 3sqrt(sin^2(θ))

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simplify sqrt(9-(3cos(θ))^2)

simplify

9 - (3 cos (θ))^{2}

3 sin^{2} (θ)

Solution steps

9 - (3 cos (θ))^{2}

Apply exponent rule:

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

= 9 - 3^{2} cos^{2} (θ)

Factor

9 - 3^{2} cos^{2} (θ) : 9 (1 - cos^{2} (θ))

= 9 (1 - cos^{2} (θ))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 9 - cos^{2} (θ) + 1

9 = 3

= 3 - cos^{2} (θ) + 1

Rewrite using trig identities

= 3 sin^{2} (θ)

15 - 7 cos (4 x + π)

\frac{e ^{2 x}}{cos ( 5 x )}

- cos (- πn)

sin (3 t - \frac{3 π}{2})

sec (\frac{2 π}{3} - θ)

What is sqrt(9-(3cos(θ))^2) ?
The solution to sqrt(9-(3cos(θ))^2) is 3sqrt(sin^2(θ))