1. Trigonometric Functions

2. Let point P with coordinates (x, y) be any point that lies on the terminal side of θ. θ is a position angle of point P Suppose P’s distance to the origin is “r” units. “r” is known as the radius vector of point P and is always considered positive

3. Trigonometric Functions By using Pythagoras Theorem, we can see that r 2 = x 2 + y 2. By taking any two of the three values for r, x, and y, we can form 6 different ratios x P(x, y) y OW r θ  opposite θ hypotenuse   adjacent θ

4. Trigonometric Functions There are 6 trigonometric functions Primary RatiosReciprocal Ratios Sine θ = Cosine θ = Tangent θ = Cosecant θ = Secant θ = Cotangent θ =

5. Trigonometric Functions Example 1: If θ is the position angle of the point P(3, 4), find the values of the six trigonometric functions of θ. Solution: To determine the values of the six trigonometric functions, we first need: 1) The values of x, y (the coordinates of a point on the terminal side of θ 2) The value of r (the distance of the point from the origin)

6. Trigonometric Functions Since P(3, 4) lies on the terminal side of θ, we know that x = 3, and y = 4. Since r 2 = x 2 + y 2  r 2 = (3) 2 + (4) 2 r 2 = 9 + 16 r 2 = 25  r = 5 Thus:

7. Trigonometric Functions Example 2: If and θ is a third quadrant angle, find the value of the other trigonometric functions of θ. Solution: Because θ is in the 3 rd quadrant, we know that the values of x and y are both negative.  r 2 = x 2 + y 2  r 2 = (12) 2 + (5) 2 r 2 = 169  r = 13

8. Trigonometric Functions Therefore, the other trigonometric functions are:

9. Homework Do # 1 – 15 odd numbers only on page 231 from Section 7.3 for Monday June 8 th