Coordinate Trigonometric Definitions If P(x, y) is any point on the terminal side of an angle in standard position and r is the distance of P from the origin, then the six trigonometric functions can be defined in terms of x, x, y, y, and r.r. x y I’m not sure I like the sound of that. That doesn’t sound much better. P(x, y) r x y

Coordinate Trigonometric Example If P(4, -3) is a point on the terminal side of an angle, find the values of the sine, cosine, and tangent of the angle. x y I think I can do this. P(4, -3) 4 -3 r Remember the Pythagorean Theorem. That was easy

More Coordinate Trigonometric Examples The given point is on the terminal side of an angle. Find; 12 5 r r r That was easy

Homework Page 367: 1 – 8

The 45 – 45 Right Triangle The 45 – Right Triangle has two 45 o angles, and two congruent sides opposite those angles. Example 1: Given one leg Example b: Given the hypotenuse That was easy

The Right Triangle The Right Triangle has a 30 o angle, and a 60 o angle Example 1: Given one leg Example b: Given the hypotenuse That was easy

Trigonometric Functions of 45 Degrees Let’s take another look at the right triangle That’s pretty easy, but I bet it’s really important.

Trigonometric Functions of 30 and 60 Degrees Let’s take another look at the right triangle That’s a little more work, but it’s still pretty easy, and I’m sure it’s really important.

Summary of the Trigonometric Functions of Special Angles

Special Angle Examples Find the exact value of the six trigonometric functions for each.

Homework Page 380:

Reference Angles The reference angle is the acute angle whose vertex is the origin and whose sides are the terminal side of the original angle and the x-axis.The reference angle is denoted as Quadrant I II Quadrant IIIQuadrant IV

More Special Angle Examples Quadrant IIIQuadrant IIQuadrant IV Quadrant II That was easy

More Special Angle Examples Quadrant IIQuadrant III Quadrant IV Quadrant II That was easy

Homework Page 395:

30 o (1, 0) 360 o 90 o 180 o 270 o Since (x, y) is really Then the x-coordinate is cos30 and the y-coordinate is sin30 (0, 1) 60 o Since (x, y) is really Then the x-coordinate is cos60 and the y-coordinate is sin60 45 o Since (x, y) is really Then the x-coordinate is cos45 and the y-coordinate is sin45

360 o 90 o 180 o 270 o (1, 0) (0, 1) (0, -1) (-1, 0)

Homework Angles & Coordinates Worksheet