1. SOHCAHTOA

2.  Write down everything you know about triangles.  Include any vocabulary related to triangles that you may have learned.  Include Diagrams.  Be Creative….

3. I like the Nick Name RATS!

4.  Imagine the pitcher stands at the pitcher’s mound at one of the acute angles. S/he throws the ball to the side which is opposite to him/her. Pitcher’s Mound opposite

5.  From the opposite side, the player throws the ball to the player at the hypotenuse. 1 1 Pitcher’s Mound opposite 2 2 3 3 hypoteneuse

6.  The player at the hypotenuse throws the ball to the last side of the triangle which is the adjacent. 1 1 Pitcher’s Mound Opposite 2 2 3 3 Hypoteneuse 4 4 Adjacent

7.  Every right angled triangle has three sides labelled from a reference angle. Hypoteneuse Opposite Adjacent Reference Angle

8.  What happens if we move the reference angle?  Discuss this with a partner? How does this change the labels on the sides? Reference Angle

9.  The adjacent and the opposite are switched!  The Hypotenuse stays the same! Reference Angle Adjacent Hypotenuse—doesn’t change! Opposite

10.  Label all the three sides from the reference angle. H H A A O O

11. A A

14. Here is a quick way to remember the sides that correspond to each ratio. S O H C A H T O A

15.  Have you noticed three buttons on your calculator? Sin Cos Tan These buttons relate to the three trig ratios we have shown from the RATS.

16.  The calculator can calculate the ratio for any given angle instantly. Sin Cos Tan Find the sin 98 °. You may need to determine if you press the sin button or enter 98 first. Try this on your calculator: Answer is: 0.990268068

17.  Check to see if your calculator is in the wrong mode.  ✔ Right Mode: Degree, D, Deg  ✗ Wrong Modes: Grad, Rad  Find your Mode Button to change it to Degrees and try the question again. Mode

18. Sin Cos Tan Find the following ratios using your calculator to 4 decimals: sin 45°= cos 60°= tan 57°= 0.7071 0.5 1.5398

19. Sin-1 Cos-1 Tan-1 Find the above buttons on your calculator. They may be above your sin/cos/tan keys. You may need to use a Second Function Key or another key to access these additional functions on your calculator. These buttons help you find the angle if you are given the trig ratio. I call this ‘going backwards’.

20. Sin-1 Cos-1 Tan-1 Let’s try the following example. Find the angle if: Method 1: Enter 4 ⁄ 5 on your calculator and enter second function sin Method 2: Enter second function sin ( 4 ⁄ 5) on your calculator ANSWER: 53.13 degrees

21.  What are the three trig ratios from the reference angle. 5 4 3

23.  Find the three ratios from the following triangle. 8 1214 ✔ ✔

25. √√ 715 ✔A✔A ✔A✔A S O H C A H T O A S O H C A H T O A Starting at the reference angle decide which two sides you have. Pick the trig ratio that uses those two sides. O H

26.  Ask yourself: What sides do I have?  Which Trig Ratio uses those two sides! 6 25 ✔B✔B ✔B✔B

27. 36 25 ✔C✔C ✔C✔C Ask yourself: What sides do I have? Which Trig Ratio uses those to sides!

28.  Find the missing side x. 56° 20 X

29.  Have: Hypoteneuse  Need: Adjacent  Use the Cosine Ratio 56° 20 X

30. 56° 20 X

31. 56° 20 X

32.  Find the missing side x. 35° x 12

33. What is the side you have and what is the side you need? Have: Opposite Need: Hypotenuse Use the Sine Ratio 35° x 12

34.  The ratio that uses both the O and the H is the sin ratio. 35° X is the hypotenuse12 is the opposite side

35.  Now we can fill in the ratio: 35° X12

36.  Now we can fill in the ratio: Solve for x in the above equation by using the ‘Switcheroo’

37.  If the side you are missing is in the NUMERATOR such as: Then multiply the two values together x=sin 43 x 12

38.  If the side you are missing is in the DENOMINATOR such as: Then use the ‘switcheroo’ to switch the cos 43 and the x Answer would be 7÷(cos 43)

39.  Case 1: Multiply ×  Case 2: Switcheroo ÷

40. II hope this was everything you needed to know about trigonometry!