Question Using the identity sin^2Theta +cos^2Theta =1 find the value of cosTheta to the nearest hundredth , if sinTheta =0.54 and 0lt Theta lt (pi )/(2) 0.08

Question

Answer 1

We are given that

and

. We are asked to find the value of

using the identity

.Since

, we have

\sin^2\Theta = (0.54)^2 = 0.2916

Substituting this into the identity, we get

0.2916 + \cos^2\Theta = 1

\cos^2\Theta = 1 - 0.2916

\cos^2\Theta = 0.7084

Since

,

is in the first quadrant, where cosine is positive. Therefore, we take the positive square root:

\cos\Theta = \sqrt{0.7084}

\cos\Theta \approx 0.84

Rounding to the nearest hundredth, we get

.Final Answer: The final answer is

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