What is sqrt((rcos(θ))^2+(rsin(θ))^2) ?

The solution to sqrt((rcos(θ))^2+(rsin(θ))^2) is r

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simplify sqrt((rcos(θ))^2+(rsin(θ))^2)

simplify

(r cos (θ))^{2} + (r sin (θ))^{2}

r

Solution steps

(r cos (θ))^{2} + (r sin (θ))^{2}

(r cos (θ))^{2} = r^{2} cos^{2} (θ)

(r sin (θ))^{2} = r^{2} sin^{2} (θ)

= r^{2} cos^{2} (θ) + r^{2} sin^{2} (θ)

Factor out common term

r^{2}

= r^{2} (cos^{2} (θ) + sin^{2} (θ))

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

r^{2} (cos^{2} (θ) + sin^{2} (θ)) = r^{2} cos^{2} (θ) + sin^{2} (θ)

= r^{2} cos^{2} (θ) + sin^{2} (θ)

Apply radical rule:

a^{2} = a,

assuming

a \geq 0

r^{2} = r

= r cos^{2} (θ) + sin^{2} (θ)

Simplify

cos^{2} (θ) + sin^{2} (θ) : 1

= r \cdot 1

Apply rule:

a \cdot 1 = a

= r

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What is sqrt((rcos(θ))^2+(rsin(θ))^2) ?
The solution to sqrt((rcos(θ))^2+(rsin(θ))^2) is r