NOTE: Here is a bunch of videos I recorded a while ago, which is why they look kinda weird. They are from precalculus 11, and could be useful if you forgot everything from trigonometry since last year.

• adj = x, opp = y, hyp = r
• SOH CAH TOA
  • sinθ = opp/hyp = y/r
  • cosθ = adj/hyp = x/r
  • tanθ = opp/adj = y/x
• from the pythagorean theorem: x^2 + y^2 = r^2

Standard Position

• angles in standard position are measured counterclockwise from the positive x-axis

Special Angles 0°, 30°, 45°, 60°, 90° Explaination

Special Angles Summary

• it is very important to remember the trigonometric ratios for the special angles, whether you memorize them, use a pattern to help you recreate the chart, or draw a 30° 60° 90° triangle and 45° 45° 90° triangle as seen in the previous video

Tangent Equation

• tanθ = sinθ/cosθ

Reference Angles

• a reference angle is the angle a terminal arm makes with the x-axis
• angles with the same reference angle have the same trigonometric ratios, except it may be positive or negative depending on the quadrant (see the next video)

Trigonometric Ratios in Quadrant 2, 3, and 4

• angles in quadrant 2, 3, and 4 have the same trigonometric ratios as the angle in quadrant 1 that has the same reference angle, but in certain cases, it will be negative

Trigonometric Ratios of Angles with Reference Angle 30°

Trigonometric Ratios of Angles with Refernce Angle 45°

Trigonometric Ratios of Angles with Reference Angle 60°

Trigonometric Ratios of 90°, 180°, 270°, 360°

Find Trigonometric Ratios Given Coordinates Example #1

• use pythagorean theorem to find 3rd side of triangle
• plug into ratios
• P(-7, 4)

Example #2

P(-3, -5)

Example #3

• P(6, -3)