1. Trigonometric Functions Section 4.2a

2. Remind me…from geometry: What does it mean for two figures to be similar ???  Same shape, but not necessarily same size… The concept of similar triangles is the basis of right triangle trigonometry, the topic of this section.

3. Right Triangle Trigonometry Standard Position (of an acute angle) – in the xy-plane, the vertex is at the origin, one ray is along the positive x-axis, and the other ray extends into the first quadrant. Example:

4. Right Triangle Trigonometry Let be an acute angle in the right . Then B sine Hyp. cosine Opp. tangent A Adj. C

5. Right Triangle Trigonometry Let be an acute angle in the right . Then B cosecant Hyp. secant Opp. cotangent A Adj. C

6. Two Famous Triangles The isosceles right triangle: Let’s find all 6 trig. functions for a angle. 1 1

7. Two Famous Triangles The isosceles right triangle: Let’s find all 6 trig. functions for a angle. 1 1

8. Two Famous Triangles The 30-60-90 triangle: Let’s find all 6 trig. functions for a angle. 2 1

9. Two Famous Triangles The 30-60-90 triangle: Let’s find all 6 trig. functions for a angle. 2 1

10. Two Famous Triangles The 30-60-90 triangle: Is there a shortcut for finding the trig. functions for a angle? 2 1

11. Using one trig ratio to find them all Let be an acute angle such that . Evaluate the other five trigonometric functions of . What does the triangle look like? Solve for x: 6 5 x

12. Evaluating Trig Functions with a Calculator Beware these common errors!!! 1. Using the calculator in the wrong mode (degrees/radians) 2. Using the inverse trig keys for cot, sec, and csc –1 Ex: the TAN is not the cotangent function!!! 3. Using incorrect shorthand Ex: to evaluate , you must type 4. Not closing parentheses

13. Getting an “exact answer” on a calculator Find the exact value of on a calculator. First, type in  Make sure you’re in degree mode!!! Next, square your answer  You should get 0.75 This suggests that the exact value of is: