Trigonometric Functions

1. Trigonometric Functions

2. Trigonometric Functions • 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 r2 = x2 + y2. • By taking any two of the three values for r, x, and y, we can form 6 different ratios P(x, y) hypotenuse  r y  opposite θ θ O x W  adjacent θ

4. Trigonometric Functions • There are 6 trigonometric functions

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: • The values of x, y (the coordinates of a point on the terminal side of θ • 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 r2 = x2 + y2 r2 = (3)2 + (4)2 r2 = 9 + 16 r2 = 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 3rd quadrant, we know that the values of x and y are both negative.  r2 = x2 + y2 r2 = (12)2 + (5)2 r2 = 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 8th