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If z gt 0, a =zcostheta, and b=zsintheta...

If `z gt 0, a =zcostheta, and b=zsintheta,` then `sqrt(a^(2)+b^(2))`=

A

1

B

z

C

2z

D

`zcostheta sin theta`

Text Solution

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The correct Answer is:
B
`a^(2)=z^(2)cos^(2)theta and b^(2)=z^(2)sin^(2)theta,` so `a^(2)+b^(2)=z^(2)(cos^(2)theta+sin^(2)theta)=z^(2)` because `cos^(2)theta+sin^(2)theta=1`. Since `sqrt(z^(2))=z` when zgt0, the correct answer choice is choice B.
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