θ

Trigonometric Ratios

θ Reference Angle Adjacent Leg Hypotenuse Opposite Leg Basic ratio definitions

+ Counter clockwise - clockwise Initial Ray Terminal Ray Definition of an angle

Coterminal angles – angles with a common terminal ray Initial Ray Terminal Ray

Coterminal angles – angles with a common terminal ray Initial Ray Terminal Ray

Radian Measure

r r 1 Radian  57.3 o 360 o = 2 π radians 180 o = π radians Definition of Radians C= 2 πr C= 2 π radii C= 2 π radians

Converting Degrees ↔ Radians Recall Converts degrees to Radians Converts Radians to degrees more examples

Unit Circle – Radian Measure

Degrees

Circle Trigonometry Definitions (x, y) Radius = r Adjacent Leg = x Opposite Leg = y reciprocal functions

Unit - Circle Trigonometry Definitions (x, y) Radius = 1 Adjacent Leg = x Opposite Leg = y 1

Unit Circle – Trig Ratiossincostan (+, +) (-, -) (-, +) (+, -) Reference Angles Skip π/4’s

Unit Circle – Trig Ratiossincostan (+, +) (-, -) (-, +) (+, -)

Unit Circle – Trig Ratiossincostan (+, +) (-, -) (-, +) (+, -) sincostan Ø Ø (0, -1) (0, 1) (1, 0)(-1, 0) 0 /2 π Quadrant Angles View π/4’s

Unit Circle – Radian Measuresincostan (+, +) (-, -) (-, +) (+, -) Degrees 1 sincostan Ø Ø 0 /2 π Quadrant Angles

A unit circle is a circle with a radius of 1 unit. For every point P(x, y) on the unit circle, the value of r is 1. Therefore, for an angle θ in the standard position:

Special Right TrianglesThe Pythagoreans Graphs Rene’ DesCartes Trigonometry Hipparchus, Menelaus, Ptolemy

Reference Angle Calculation 2 nd Quadrant Angles3 rd Quadrant Angles4 th Quadrant Angles Return

Unit Circle – Degree Measure 0/ Return

Unit Circle – Degree Measure 0/ sincostan (+, +) (-, -) (-, +) (+, -) Return 1 sincostan Ø Ø 0/ Quadrant Angles

Ex. # 6Ex. # 5 Ex. # 4Ex. # 3 return

Circle Trigonometry Definitions – Reciprocal Functions (x, y) Radius = r Adjacent Leg = x Opposite Leg = y return

Unit Circle – Radian Measure 1