1. Introduction to Trigonometric Functions
Return to home page

2. Trig functions are the relationships amongst various sides in right triangles.
You know by the Pythagorean theorem that the sum of the squares of each of the smaller sides equals the square of the hypotenuse,

3. You know in the above triangle that
Trig functions are how the relationships amongst the lengths of the sides of a right triangle vary as the other angles are changed.

4. How does this relate to trig?
The opposite side divided by the hypotenuse, a/c, is called the sine of angle A
The adjacent side divided by the hypotenuse, b/c, is called the cosine of Angle A
The opposite side divided by the adjacent side, a/b, is called the tangent of Angle A

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

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

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

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

9. 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?

10. 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.

11. 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

12. GREAT JOB! Next question
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

13. 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

14. 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

15. 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 question

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

17. 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

18. 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

19. 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

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

21. 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

22. Great job! Go to next section
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

23. Introduction to Quadrants
90 degrees II I
180 degrees______________________ 0 degrees
__________________ IV
III
270 degrees

24. Quadrants All angles are divided into 4 quadrants
Angles between 0 and 90 degrees are in quadrant 1
Angles between 90 and 180 degrees are in quadrant II
Angles between 180 and 270 degrees are in quadrant III
Angles between 270 and 360 degrees are in quadrant IV
Why is this important? Click and find out!

25. Importance of quadrants
Different trig functions are positive and negative in different quadrants.
The easy way to remember which are positive and negative in each quadrant it to remember, “All Students Take Classes”

26. All Students Take Classes
Quadrant I: 0 – 90 degrees: All: All trig functions are positive
Quadrant II: 90 – 180 degrees: Students: Sine functions are positive
Quadrant III: 180 – 270 degrees: Take: Tangent functions are positive
Quadrant IV: 270 – 360 degrees: Classes; Cosine functions are positive

27. Standard Angle Values
Angle 30 45 60 90
Sine
Cosine
Tangent

28. Remember Simplify the fractions
Place the radicals in the numerator. Write
Instead of

29. 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