1. Right Triangle Trigonometry

2. Unit Circle Definitions of the 6 Trig. Functions… sin = y cos = x tan = yxyx csc = 1y1y sec = 1x1x cot = xyxy

3. Non-Unit Circle Definitions of the 6 Trig. Functions… tan = yxyx csc = ryry sec = rxrx cot = xyxy sin = yryr cos = xrxr

4. sin = yryr cos = xrxr These definitions are closely related to the unit circle definition. In the unit circle, the radius is = to 1, thereby eliminating the denominator.

5. Since this is a unit circle (radius of one), sin 45  =  2 / 2 (2/2, 2/2)(2/2, 2/2) (-1,0)  (0,1)  (0,-1)  (1,0) 45   (2,0)  (  2,  2) Now, on this second circle, the radius is no longer 1 unit (it’s 2). Therefore, sin 45  = y / r or sin 45  =  2 / 2

6. Let’s practice these definitions. Find exact values of the six trig. functions of the angle  shown in the figure. 12 5 If this triangle was placed at the center of a circle, what would the radius of that circle be? a 2 +b 2 = c 2 12 2 +5 2 = c 2 169 = c 2 13 = c 13 (12,5)  sin  = yryr cos  = xrxr tan  = yxyx csc  = ryry cos  = rxrx cot  = xyxy = 5 13 = 12 13 = 5 12 = 13 5 = 13 12 = 5 

7. Your Turn #1: Place your work in your notebook. Find exact values of the six trig. functions of the angle  shown in the figure. 5 5 Look back at the previous slide if you need assistance. 

8. Your Turn #2: Place your work in your notebook. Find exact values of the six trig. functions of the angle  shown in the figure. 8 4  Hint: Be sure to reduce radicals.

9. Let’s practice some more… Sketch a right triangle corresponding to the trig. function of the acute angle . Then determine the other five trig. functions of . sin  = 2323 = yryr 2 3 a 2 + b 2 = c 2 a 2 + 2 2 = 3 2 a 2 + 4 = 9 a 2 = 5 a =  5 55 (  5,2)  cos  = xrxr = 5353 tan  = yxyx = 255255 csc  = ryry = 3232 sec  = rxrx = 355355 cot  = xyxy = 5252 

10. Your Turn #3: Place your work in your notebook. Look back at the previous slide if you need assistance. Sketch a right triangle corresponding to the trig. function of the acute angle . Then determine the other five trig. functions of . sec  = 4 Think sec  = 4 / 1

11. Your Turn #4: Place your work in your notebook. Look back if you need assistance. Sketch a right triangle corresponding to the trig. function of the acute angle . Then determine the other five trig. functions of . csc  = 9595

12. What is SOH CAH TOA? This is another way of remembering the definitions of the trigonometric functions. SOH sin  = opposite hypotenuse Opp.  Hyp.

13. What is SOH CAH TOA? CAH cos  = adjacent hypotenuse Adj.  Hyp.

14. What is SOH CAH TOA? TOA tan  = opposite adjacent Adj.  Opp.

15. Assignment: pg. 156: 1-26