Answer:
- sin(θ) = (√7)/4
- tan(θ) = (-√7)/3
Explanation:
You want the sine and tangent of the 2nd-quadrant angle whose cosine is -3/4.
Identities
The relevant trig identities are ...
sin(θ) = ±√(1 -cos(θ)²) . . . . . the + sign applies in the 2nd quadrant
tan(θ) = sin(θ)/cos(θ)
Application
Using the given value of cosine, we find the sine to be ...
sin(θ) = √(1 -(-3/4)²) = √(7/16)
sin(θ) = (√7)/4
and
tan(θ) = sin(θ)/cos(θ) = ((√7)/4)/(-3/4)
tan(θ) = (-√7)/3
<95141404393>