Download Objective#1: Find the value of the six trigonometric functions

Objective#1: Find the value of the six trigonometric functions.
Objective #2: Find the value of the six trigonometric functions of an angle in
standard position given a point on its terminal side.
The Unit Circle
9 A unit circle is a circle with
radius 1 and center (0,0).
9 The unit circle can be used to
evaluate many trig values
without the use of a calculator.
9 In the unit circle,
o
sin θ =
o
cos θ =
o
tan θ =
o
csc θ =
o
sec θ =
o
cot θ =
Using Special Right Triangles and Reference Angles to Evaluate Trig
Functions
9 Rewrite the function in terms of
it’s reference angle
o Make sure you include
the correct sign of your
answers.
ƒ All (QI)
ƒ Students (QII)
ƒ Take (QIII)
ƒ Calculus (QIV)
9 Use your 30-60-90 or 45-45-90
to write a ratio for the trig
function.
Examples: Find the exact value of each trig function.
1. tan ( 225° )
2. sec ( −90° )
3. sin 300°
4. cot(−30°)
5. csc ( −180 ) °
6. cos 315°
Example:
7. Find the values of the six trigonometric functions for angle θ in standard
position if the point ( −6,6 ) lies on its terminal side.
Example:
8. Find the remaining five trigonometric functions in simplest radical form if
1
cos θ = − and 90° < θ < 180° .
5