1. WARM UP
Use special triangles to evaluate:

2. What you’ll learn about
Trigonometric Functions of Any Angle
Quadrantal Angles
Using One Trig Ratio to Find the Others
Signs of Trig Ratios in Quadrants
… and why
Trigonometry is a mathematical tool that allows us to solve real-world problems involving right triangle relationships…we can now move beyond acute angles, to consider any angle

3. Trigonometric Functions of any Angle
If P(x, y) is a point on the terminal side of an angle θ and r is the distance from P to the origin
What is sin θ in terms of x, y and/or r?
What is cos θ in terms of x, y and/or r?
What is tan θ in terms of x, y and/or r?

4. Trigonometric Functions of any Angle

5. Trig Functions of Quadrantal Angles
A quadrantal angle is an angle whose terminal side is on the x- or y-axis
Examples: Find each of the following, if it exists. If the value is undefined, write “undefined”
sin (– 270˚)
tan 3π
sec 11π/2

6. Evaluating Trig Functions of Quadrantal Angles

7. y
P(1, 1)
45° 1 x

8. y
P(–1, 1)
P(1, 1)
45° 1
45° 1
45° 1
45° 1 x
P(–1, –1)
P(1, –1)

9. y
30° 2 1 x

10. y 2
60° x 1

11. Trig Signs in Four Quadrants
Sine Positive
All Positive
Tangent Positive
Cosine Positive
“All Students Take Calculus”

12. Using One Trig Ratio to Find the Others
Find cos and tan by using the given information to construct a reference triangle

13. HOMEWORK Page 381 # 37 to 45 EXIT TICKET
What is sin θ in terms of x, y and/or r?
What is cos θ in terms of x, y and/or r?
What is tan θ in terms of x, y and/or r?