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5 votes
Given cos theta = √3/4 and sin theta < 0. What is the value of sin theta? ​

2 Answers

6 votes

Answer:

see explanation

Explanation:

Using the trigonometric identity

• sin²x + cos²x = 1 ⇒ sin x = ±
√(1-cos^2x)

Since sinΘ < 0 , then

sinΘ = -
\sqrt{1-((√(3) )/(4))^2 }

= -
\sqrt{1-(3)/(16) }

= -
\sqrt{(13)/(16) } = -
(√(13) )/(4)

User Budamivardi
by
8.1k points
4 votes

Answer:


\sqrt{ (13)/(16) }

Explanation:


cos \: theta = ( √(3) )/(4) \\ sin \: theta = \sqrt{1 - {cos}^(2) theta} \\ = \sqrt{1 - {( ( √(3) )/(4) ) }^(2)} \\ = \sqrt{1 - (3)/(16)} \\ = \sqrt{ (13)/(16) }

User Senal
by
8.4k points

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