22. use the unit - circle below to determine the cosine of π/3. (0,1) (1/2,√3/2) 120° 90° 60° 45°…
22. use the unit - circle below to determine the cosine of π/3. (0,1) (1/2,√3/2) 120° 90° 60° 45° (√2/2,√2/2) (-1/2,√3/2) (√2/2,√2/2) 2π/3 π/3 π/4 135° 3π/4 (-√2/2,√2/2) 30° (√3/2,1/2) (-√3/2,1/2) 150° 5π/6 (-1,0) 180° π 0,2π (1,0) 11π/6 7π/6 210° 5π/4 (-√2/2,-√2/2) 225° 4π/3 (-√3/2,-1/2) 330° 7π/4 315° (√2/2,-√2/2) (√3/2,-1/2) 5π/3 300° 3π/2 270° (-√2/2,-√2/2) 240° (-1/2,-√3/2) (0, - 1) (1/2,-√3/2) √3/3 √3/2 √3 1/2
Answer
Explanation:
Step1: Locate angle on unit - circle
The angle $\frac{\pi}{3}$ (or 60°) is located in the first - quadrant of the unit circle.
Step2: Recall cosine definition on unit - circle
For a point $(x,y)$ on the unit circle corresponding to an angle $\theta$, $\cos\theta=x$.
Step3: Find the $x$ - coordinate
The point on the unit circle corresponding to the angle $\frac{\pi}{3}$ is $(\frac{1}{2},\frac{\sqrt{3}}{2})$. So, $\cos\frac{\pi}{3}=\frac{1}{2}$.
Answer:
$\frac{1}{2}$