If cos θ = 4/5 and θ lies in 4th quadrant them sin θ = ____?
- -4/3
- -3/5
- 3/5
- None of these
Explanation
Given cos θ = 4/5 and θ lies in the 4th quadrant.
In the 4th quadrant, cosine is positive, and sine is negative.
We know that sin² θ + cos² θ = 1
sin² θ = 1 - cos² θ
= 1 - (4/5)²
= 1 - 16/25
= 9/25
sin θ = ±√(9/25)
= ±3/5
Since θ lies in the 4th quadrant, sin θ is negative:
sin θ = -3/5
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