Question

Cos (theta) = sqrt2/2, and 3pi/2

Answer 1

see explanation

Explanation:

Using the trigonometric identities

sin²x + cos²x = 1 ⇒sinx = ±
`√(1-cos^2x)` and

tanx =
`(sinx)/(cosx)`

Given

cosΘ =
`(√(2) )/(2)`, then

sinΘ = ±
`\sqrt{1-((√(2) )/(2))^2 }`

Since
`(3\pi )/(2)` < Θ < 2π ← fourth quadrant

Then sinΘ and tanΘ are both negative

sinΘ = -
`\sqrt{1-(1)/(2) }`

= -
`(1)/(√(2) )` = -
`(√(2) )/(2)`

----------------------------------------------------------------------------

tanΘ =
`(-√(2) )/(2)` ÷
`(√(2) )/(2)`

= -
`(√(2) )/(2)` ×
`(2)/(√(2) )` = - 1

Answer 2

sin theta= -sqrt2/2

tan theta=-1

Explanation:

I just did it.