WARM UP Use special triangles to evaluate:

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

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?

Trigonometric Functions of any Angle

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

Evaluating Trig Functions of Quadrantal Angles

y P(1, 1) 45° 1 x

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

y 30° 2 1 x

y 2 60° x 1

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

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

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?