The Unit circle. Def: If the terminal side of an angle is in standard position and intersects the unit circle at P(x,y) then x = cos Ɵ and y = sin Ɵ Trig.

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Presentation transcript:

The Unit circle

Def: If the terminal side of an angle is in standard position and intersects the unit circle at P(x,y) then x = cos Ɵ and y = sin Ɵ Trig functions defined using the unit circle are called circular functions.

1.) Find the exact values for the trig functions for 45 o

2.) Find the exact values for the trig functions:

Def: Quadrantal Angles: Angles whose terminal side coincides with either the x-axis or the y-axis are called quadrantal angles.

A S T C - All Students Take Calculus!

Def: Trigonometric Identities: The trigonometric identities are relationships which are true for all values of the variables for which the expressions are defined.

3. Use trig identities to simplify the following

Suggestions Change everything to sine and cosine Substitute basic trig identities Factor or foil the expression Multiply both numerator and denominator by the same thing Find a common denominator for sums and differences

Homework Practice worksheet: The Unit Circle