Question

Given cosθ = -(√24/5) and angle θ is in Quadrant III, what is the exact value of sinθ in simplest form? Simplify all radicals if needed.

Answer 1

`sin \theta = - (1)/(5)`

Explanation:

We Know

`sin ^2 \theta + cos^2 \theta = 1\\`

`sin^2 \theta = 1 - cos^2 \theta`

`= 1 - (-(√(24) )/(5))^2`
`[\ given : cos \theta = -(√(24) )/(5) \ ]`

`= 1 - (24)/(25)\\\\= (25 - 24)/(25)\\\\=(1)/(25)`

`sin ^2 \theta = (1)/(25)\\\\sin \theta = \sqrt {(1)/(25)}\\\\sin \theta = \pm (1)/(5)\\\\Since \ \theta \ is \ in \ III \ Quadrant \ sin \theta = -(1)/(5)`