Question

express cos theta in terms of sin theta​

Answer 1

Answer:

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Answer 2

$cos$∅ =  $\sqrt{1 - sin^{2} }$∅

Given: $cos$∅ and $sin$∅

To find: Value of $cos$∅ in terms of $sin$∅

Solution:

We know that using trigonometric identities,

∵ $cos^{2}$∅ + $sin^{2}$∅ = 1

Taking $sin^{2}$∅ to right-hand side

⇒  $cos^{2}$∅ = 1 -  $sin^{2}$∅

Taking square root on both sides

⇒ $\sqrt{cos^{2} }$∅ = $\sqrt{1 - sin^{2} }$∅

Square of $cos$∅ will eliminate the square root

⇒ $cos$∅ = ±  $\sqrt{1 - sin^{2} }$∅

Now we know that ∅ < 90° i.e., is an acute angle and $cos$∅ will be positive when ∅ is acute.

∴ $cos$∅ = $\sqrt{1 - sin^{2} }$∅

Hence, $cos$∅ in terms of $sin$∅ is  $\sqrt{1 - sin^{2} }$∅.

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