Find the terminal point on the unit circle determined by π6 radians.Use exact values, not decimal approximations.
Question
Find the terminal point on the unit circle determined by radians.
Use exact values, not decimal approximations.
Solution
The terminal point on the unit circle determined by π/6 radians can be found using the unit circle definitions of sine and cosine.
Step 1: Identify the angle The angle given is π/6 radians.
Step 2: Convert the angle to degrees if necessary In this case, it's not necessary because the angle is already given in radians.
Step 3: Use the unit circle to find the coordinates On the unit circle, the x-coordinate is equal to cos(θ) and the y-coordinate is equal to sin(θ). For an angle of π/6 radians, cos(π/6) = √3/2 and sin(π/6) = 1/2.
So, the terminal point on the unit circle determined by π/6 radians is (√3/2, 1/2).
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