1. Trigonometry Basics Right Triangle Trigonometry

3. Sine Function When you talk about the sin of an angle, that means you are working with the opposite side, and the hypotenuse of a right triangle.

4. Sine function Given a right triangle, and reference angle A: sin A = A opposite hypotenuse The sin function specifies these two sides of the triangle, and they must be arranged as shown.

5. Sine Function For example to evaluate sin 40°… Type-in 40 on your calculator (make sure the calculator is in degree mode), then press the sin key. It should show a result of 0.642787… –Note: If this did not work on your calculator, try pressing the sin key first, then type-in 40. Press the = key to get the answer.

6. Sine Function Try each of these on your calculator: sin 55° sin 10° sin 87° Sine Function

7. Try each of these on your calculator: sin 55° = 0.819 sin 10° = 0.174 sin 87° = 0.999 Sine Function

8. Inverse Sine Function Using sin -1 (inverse sin): If 0.7315 = sin θ then sin -1 (0.7315) = θ Solve for θ if sin θ = 0.2419 Inverse Sine Function

9. Cosine function The next trig function you need to know is the cosine function (cos): cos A = A adjacent hypotenuse Cosine Function

10. Use your calculator to determine cos 50° First, type-in 50… …then press the cos key. You should get an answer of 0.642787... –Note: If this did not work on your calculator, try pressing the cos key first, then type-in 50. Press the = key to get the answer. Cosine Function

11. Try these on your calculator: cos 25° cos 0° cos 90° cos 45° Cosine Function

12. Try these on your calculator: cos 25° = 0.906 cos 0° = 1 cos 90° = 0 cos 45° = 0.707 Cosine Function

13. Using cos -1 (inverse cosine): If 0.9272 = cos θ then cos -1 (0.9272) = θ Solve for θ if cos θ = 0.5150 Inverse Cosine Function

14. Tangent function The last trig function you need to know is the tangent function (tan): tan A = A adjacent opposite

15. Use your calculator to determine tan 40° First, type-in 40… …then press the tan key. You should get an answer of 0.839...  Note: If this did not work on your calculator, try pressing the tan key first, then type-in 40. Press the = key to get the answer.

16. Tangent Function Try these on your calculator: tan 5° tan 30° tan 80° tan 85°

17. Tangent Function Try these on your calculator: tan 5° = 0.087 tan 30° = 0.577 tan 80° = 5.671 tan 85° = 11.430

18. Using tan -1 (inverse tangent): If 0.5543 = tan θ then tan -1 (0.5543) = θ Solve for θ if tan θ = 28.64

19. Remember SOHCAHTOA Sine is Opposite divided by Hypotenuse Cosine is Adjacent divided by Hypotenuse Tangent is Opposite divided by Adjacent SOHCAHTOA!!!!!!

20. Table of Contents Examples Question 1 Question 2 Question 3 Question 4

21. Example 1 If a = 3 and c = 6, what is the measurement of angle A?

22. Answer: a/c is a sine relationship with A. Sine A = 3/6 =.5, from your calculator, angle A = 30 degrees.

23. Example 2 A flagpole casts a 100 foot shadow at noon. Lying on the ground at the end of the shadow you measure an angle of 25 degrees to the top of the flagpole. How High is the flagpole?

24. How do you solve this question? You have an angle, 25 degrees, and the length of the side next to the angle, 100 feet. You are trying to find the length of the side opposite the angle. Opposite/adjacent is a tangent relationship Let x be the height of the flagpole From your calculator, the tangent of 25 is.47.47 = x = (.47)(100), x = 47 The flagpole is 47 feet high.

25. Question 1 Given Angle A is 35 degrees, and b = 50 feet. Find c. Click on the correct answer. A. 61 feet B 87 feet C. 71 feet

26. GREAT JOB! You have an angle and an adjacent side, you need to find the hypotenuse. You knew that the cosine finds the relationship between the adjacent and the hypotenuse. Cosine 35 = 50/c, c Cosine 35 = 50, So c = 50/cos 35, or approximately 61 Next question

27. Nice try You have an angle and the adjacent side. You want to find the hypotenuse. What relationship uses the adjacent and the hypotenuse? Back to Question Back to tutorial

28. Question 2 If the adjacent side is 50, and the hypotenuse is 100, what is the angle? Please click on the correct answer. A. 60 degrees B. 30 degrees C. 26 degrees

29. Way to go! Given the adjacent side and the hypotenuse, you recognized that the adjacent divided by the hypotenuse was a cosine relationship. Cosine A = 50/100, A = 60 degrees Next questionquestion

30. Nice try Given an adjacent side and a hypotenuse, what relationship will give you the angle? Back to question Back to tutorial

31. Question 3 If the opposite side is 75, and the angle is 80 degrees, how long is the adjacent side? A. 431 B. 76 C. 13

32. Nice job You were given the opposite side of 75 and an angle of 80 degrees and were asked to find the adjacent side. You recognized that this was a tangent relationship. Tangent 80 = 75/b, b tangent 80 = 75, b = = 13 Next question

33. Nice Try You are given an angle and the opposite side, and have been asked to find the adjacent side. What relationship uses the opposite side and the adjacent side? Back to question Back to tutorial

34. Question 4: If B = 50 degrees and b = 100 what is c? A. 155 B. 130 C. 84 a b c ________ ___________ B C A

35. Nice try What is the relationship between B and b? And, what is the relationship between b and c? Return to question Return to tutorial

36. Great job! First, you recognized that b is the opposite side from B. Then, you recognized that the relationship between an opposite side and the hypotenuse is a sine relationship. Sine 50 = 100/c, c Sine 50 = 100, c = 100/sine 50 = 130. Go to next section

37. Congratulations You have learned how to use the 3 main trig functions, you have learned which functions are positive in which quadrants, and you have learned values of sine, cosine, and tangent for 5 standard angles. Return to home page