# The Circular Functions (The Unit Circle)

The Circular Functions (The Unit Circle) SECTION 4.3 DAY 1 Angle and Angle Measurements Terms Initial Side: Always on the x-axis. Terminal Side: Ending

point. Image Angle Measure Positive Angle Counterclockwis e Negative Angle Clockwise Trigonometric Functions Reference

Triangle Let be an acute angle in the right triangle . Then, Trig Functions of General Angles Exercises: #1 #4

Directions: Evaluate the six trigonometric functions of . 2 2 2 (1 , 1) + = 1 1 2

Exercises: #5 #10 Directions: Point P is on the terminal side of . Evaluate the six trigonometric functions of . P(3,4) 2 2 2 + = (3, 4 )

5 (2, 0) =2 4 UND 3 UND

HOMEWORK P. 365: #1 #10 Exit Slip Directions: Evaluate the six trigonometric functions of . 12 2 2 2 13

(5, 12) 5 + = The Circular Functions (The Unit Circle) SECTION 4.3 DAY 2 Coterminal Angles (Have the same terminal side).

Radians Degrees Positive: Add Negative: Subtract Positive: Add Negative: Subtract Example:

P: N: Example: P: N: Reference Angles Quadrant I

Quadrant II Reference Angle 9 4 or Quadrant III

Reference Angle Quadrant IV Reference Angle or Reference

Angle or The Circular Functions (The Unit Circle) SECTION 4.3 DAY 3 Warm up: Calculator Experiment Use you calculator to determine the sign of the following: (Make sure your calculator is in degrees) Group Group Group

Group #1 Quadrant # ?? #2 #3 #4 Quadrants with Positive Functions (x,-y)

Two Helpful Hints to Remember Quadrants with Positive Functions All Students Take Calculus All Silly Turtles Crawl Or make you own!! Example (Exercises #11 #14) Directions: State the sign ( of (a) (b) and (c) for values of in the interval given.

What Quadrant is this? III What trig functions are positive here? Tan and Cot a) b) c) Example 2 (Exercises #15#20) Determine the sign ( of the given value without the use of a calculator. a)

b) Two Special Triangles Trigonometric Functions Reference Triangle Let be an acute angle in the right triangle . Then,

Reference Angles Quadrant I Quadrant II Reference Angle or Quadrant III

Reference Angle Quadrant IV Reference Angle or Reference Angle

or Trigonometric Ratio worksheet Use your two special triangles and All Students Take Calculus to fill in the following chart. No calculators are allowed. Quadra Referen Degree s Radian s nt or Axis

Sketch ce Angle Sin Cos Tan Csc Sec

Cot Example 3 (Exercises #31 #42) Directions: Evaluate without using a calculator by using ratios in a reference triangle. a. cos b. 1 cos ( 480 )= 2

HOMEWORK DUE MONDAY: Worksheet Trigonometric Special Angles (Multiples of 30 and 45 degrees) Worth: 40 points Do not wait to the last minute. You are

able to do all rows except the quadrant angles i.e.. . P. 365: #11 #20 AND #31 The Circular Functions (The Unit Circle) SECTION 4.3 DAY 4 Quadrant Angles The Unit Circle Examples

We know points are always: (0,1) In the unit circle, our points are: (1,0) (1,0) (0,1) Quadrant Angles Solutions

UND UND UND UND UND UND

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