Answer:
- sin(θ) = (√21)/5
- cos(θ) = 2/5
Explanation:
You want the exact values of sine and cosine of the angle whose terminal point is at x=2/5 on the unit circle in the first quadrant.
Pythagorean identity
The coordinates of a point on the unit circle are (cos(θ), sin(θ)). You already know that the x-coordinate is 2/5, so ...
cos(θ) = 2/5
The Pythagorean identity in trigonometric terms is ...
sin²(θ) +cos²(θ) = 1
Then the sine of the angle is ...
sin(θ) = √(1 -cos²(θ))
sin(θ) = √(1 -(2/5)²) = √((25 -4)/25)
sin(θ) = (√21)/5
The exact values of sine and cosine are ...
- sin(θ) = (√21)/5
- cos(θ) = 2/5