Trigonometric Ratios in the Unit Circle 14 April 2011

Trigonometric Ratios in the Unit Circle The unit circle has a radius of 1

Trigonometric Ratios in the Unit Circle, cont. The tangent and cotangent formulas stay the same

“All Students Take Calculus” AS CT all ratios are positive sine is positive tangent is positive cosine is positive cosecant is positive cotangent is positive secant is positive

Example: Trigonometric Ratio Sine Cosine Tangent Cosecant Secant Cotangent

Example: Trigonometric Ratio Sine Cosine Tangent Cosecant Secant Cotangent

Your Turn: On the Signs of Trigonometric Ratios handout, complete the feature map and problems 1 – 3

Graphing Negative Radians Find the positive coterminal angle 1 st ! Sketch the positive coterminal angle

Graphing Negative Radians, cont.

Graphing Radians with Multiple Revolutions If the angle measure is larger than 2 pi, keep subtracting 2 from the fraction until the fraction is between 0 and 2 pi. (Find a coterminal angle between 0 and 2 pi.)

Graphing Multiple Rev. Radians, cont.

Your Turn: On the Signs of Trigonometric Ratios handout, complete the feature map and problems 4 – 9

The Cardinal Points of the Unit Circle Review

Reminder: Special Right Triangles 30° 60° 45°

Investigation! Fit the paper triangles onto the picture below. The side with the * must be on the x-axis. Use the paper triangles to determine the coordinates of the three points.

Special Right Triangles & the Unit Circle

Bottom half of circle

Special Right Triangles & the Unit Circle

Bottom Half of Circle

Evaluating Trigonometric Expressions Step 1: Substitute the correct exact value for the trigonometric function. (Use the unit circle!) Step 2: Evaluate using the order of operations

Examples