Question

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

Answer 1

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)`

Answer 2

`\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) }`