Question

The value of the cosine of an angle in Quadrant Il is given. cos theta= -2/5 What is sin theta? O- ✓29 5 V10 5 5 VI 21 5​

Answer 1

`(√(21) )/(5)`

Explanation:

Given

cosθ = -
`(2)/(5)`

Using the identity

sin²θ + cos²θ = 1 , then

sinθ = ±
`√(1-cos^20)`

= ±
`\sqrt{1-(-(2)/(5))^2 }`

= ±
`\sqrt{1-(4)/(25) }`

= ±
`\sqrt{(21)/(25) }`

= ±
`(√(21) )/(5)`

Since θ is in second quadrant the sinθ > 0 , thus

sinθ =
`(√(21) )/(5)`