MATH 12550.00 - Summer - Recitation # 7

MATH 12550.00 - Summer - Recitation # 7 - Unit Circle Review 1. Fill in the blanks: y (0, 1) (-, -) (-, -) (-, -) (-, -) (-, -) (-, -) ?/2 2?/3 ?/3 3?/4 ?/4 5?/6 90° ?/6 120° 60° 135° 45° 150° 30° (-1, 0) ? 180° 360° 2? (1, 0) x 210° 330° 7?/6 11?/6 225° 315° (-, -) 5?/4 240° 270° 300° 7?/4 (-, -) 4?/3 5?/3 3?/2 (-, -) (-, -) (-, -) (-, -) (0, -1)

Transcript

00:01 I'm going to give you an easy way to remember the values around the unit circle.

00:05 I see we already have the quadrantal angles in there.

00:08 We're going to start with the y values, which is our sign values of y.

00:12 But for my y values, i'm going to start here and see that zero is the same thing as 0 over 2.

00:18 And 1 is the same thing is 2 over 2.

00:22 Okay, so now we can think of that as the square root of 0 over 2.

00:27 We can think of this as the square root of 4 over 2.

00:30 The reason that's important is because now we can go around this unit circle and say this is going to be the square root of 1 over 2, which is 1 half.

00:41 This is the square root of 2 over 2, which is going to simply be the square root of 2 over 2.

00:47 This would be the square root of 3 over 2, which is simply the square root of 3 over 2.

00:53 Then this would become the square root of 4 over 2, which is 2 over 2 or 1.

00:59 So notice they go from 0, 1, 2, 3, 4, all under the square root and all with a denominator of 2.

01:09 We can continue this pattern, but we're going to go back down to 0.

01:14 So this would be square root of 3 over 2.

01:18 Can't simplify that.

01:20 Square root of 2 over 2, can't simplify that.

01:23 Square root of 1 over 2, well, that's going to become 1 1 1⁄2, and then square root of 0 over 2.

01:29 2, which is our 0.

01:32 We're now going to continue that pattern, but notice we're going from 0 to negative 1.

01:38 So we're going to go negative square root of 1 over 2.

01:42 Well, that'll be negative 1 half.

01:44 Negative square root of 2 over 2 can't simplify.

01:49 Negative square root of 3 over 2.

01:51 Can't simplify that.

01:53 Negative square root of 4 over 2...

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