Question

Find t for the following terminal points, 0 < t < 2π (a) P(0,1), t = __________ (b) P (-√2 / 2 , √2 / 2 ),t = ________________ (c) P(-1,0 ), t = _________________

Answer 1

The values of t for the given terminal points on the unit circle are π/2 for point P(0,1), 3π/4 for point P(-√2/2,√2/2), and π for point P(-1,0).

Step-by-step explanation:

The question requires finding the value of t for a given point on the unit circle where 0 < t < 2π.

1. For point P(0,1), the corresponding angle where the terminal side of the angle intersects this point on the unit circle is at t = π/2 or 90° because it lies on the positive y-axis.
2. For point P(-√2 / 2 , √2 / 2), this point corresponds to the terminal side of an angle in the second quadrant, where both x and y coordinates are the same absolute value but the x is negative and y is positive. The angle with these sine and cosine values is t = 3π/4 or 135°.
3. For point P(-1,0), this is on the negative x-axis, which corresponds to an angle of t = π or 180°.