What is sqrt(9-(3sin(θ))^2) ?

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

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simplify sqrt(9-(3sin(θ))^2)

simplify

9 - (3 sin (θ))^{2}

3 cos^{2} (θ)

Solution steps

9 - (3 sin (θ))^{2}

Apply exponent rule:

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

= 9 - 3^{2} sin^{2} (θ)

Factor

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

= 9 (1 - sin^{2} (θ))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 9 - sin^{2} (θ) + 1

9 = 3

= 3 - sin^{2} (θ) + 1

Rewrite using trig identities

= 3 cos^{2} (θ)

cos (2 π - θ)

sin (arccsc (x))

a tan (- 1)

tan (4 5^{\circ} + x)

sin (a - π)

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