I need help with these, please.

Question

Find the reference number for each value of t.

a) t=7pi

b)t=4

Answer 1

a) reference number (angle) for 7π DNE because 7π is quadrantal angle (it terminal side in standatd position is negative x-axis, because 7π - 3·2π = π.

b) Because π < 4 < 3π/2 angle 4 in quadrantan 3. So reference number is (4 - π)

Answer 2

Kayley,

By "reference number" I am assuming the problem is asking you to determine the REFERENCE ANGLE, measured in radians. The definition of REFERENCE ANGLE is the ACUTE ANGLE MADE BY THE TERMINAL RAY AND THE X-AXIS. Recall that an angle is made of 2 rays, and the INITIAL RAY of an angle centered at the origin is ALWAYS ON THE POSITIVE X-AXIS. So, with these assumptions in mind, here is the solution:

a) t = 7π

The angle π radians is a straight angle with the initial ray on the positive x-axis and the terminal ray on the negative x-axis. This is the same as 180 degrees. Continue circulating around counting angles by π.

1. 2π is coterminal with 0 radians.
2. 3π is coterminal with π radians.
3. 4π is coterminal with 0 radians.
4. 5π is coterminal with π radians.
5. 6π is coterminal with 0 radians
6. And finally 7π is coterminal with π radians.

Now, the question asked for a REFERENCE angle. Since this angle is aligned on the x-axis, the reference angle for angle t is 0 radians.

b) t=4

I am assuming this angle is also in radians. To determine what the reference angle is you need to know what quadrant the terminal ray of the angel falls in. Recall π is about 3.14 which is a straight angle on the negative x-axis, so 4 would be a little bit larger angle, with the terminal ray in Quadrant III. As another check, π/2 is about 1.57, so 3π/2 = approx. 3.14+1.57 > 4. Therefore, t = 4 falls in between π (180 degrees) and 3π/2 (270 degrees). Draw an angle in Quadrant III. Now, think of the geometry to find the acute angle with the x-axis. You have to subtract that angle minus 180 degrees. In radians, we have t-π.

Please reach out to me with more questions or to schedule a session! - ALISON S.