Introduction to trigonometric functions
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Introduction to Trigonometric Functions. Return to home page. 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, .

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Slide2 l.jpg


You know in the above triangle that l.jpg

You know in the above triangle that in right triangles.

Trig functions are how the relationships amongst the lengths of the sides of a right triangle vary as the other angles are changed.


How does this relate to trig l.jpg
How does this relate to trig? in right triangles.

  • 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


Remember sohcahtoa l.jpg
Remember SOHCAHTOA in right triangles.

  • Sine is Opposite divided by Hypotenuse

  • Cosine is Adjacent divided by Hypotenuse

  • Tangent is Opposite divided by Adjacent

  • SOHCAHTOA!!!!!!


Table of contents l.jpg
Table of Contents in right triangles.

  • Examples

  • Question 1

  • Question 2

  • Question 3

  • Question 4


Example 1 if a 3 and c 6 what is the measurement of angle a l.jpg
Example 1 in right triangles. If a = 3 and c = 6, what is the measurement of angle A?


Answer a c is a sine relationship with a sine a 3 6 5 from your calculator angle a 30 degrees l.jpg
Answer: a/c is a sine relationship with A. in right triangles. Sine A = 3/6 = .5, from your calculator, angle A = 30 degrees.


Example 2 l.jpg
Example 2 in right triangles.

  • 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?


How do you solve this question l.jpg
How do you solve this question? in right triangles.

  • 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.


Question 1 l.jpg
Question 1 in right triangles.

  • 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


Great job l.jpg
GREAT JOB! in right triangles.

  • 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


Nice try l.jpg
Nice try in right triangles.

  • 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


Question 2 l.jpg
Question 2 in right triangles.

  • 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


Way to go l.jpg
Way to go! in right triangles.

  • 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


Nice try16 l.jpg
Nice try in right triangles.

  • Given an adjacent side and a hypotenuse, what relationship will give you the angle?

Back to question

Back to tutorial


Question 3 l.jpg
Question 3 in right triangles.

  • If the opposite side is 75, and the angle is 80 degrees, how long is the adjacent side?

  • A. 431

  • B. 76

  • C. 13


Nice job l.jpg
Nice job in right triangles.

  • 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


Nice try19 l.jpg
Nice Try in right triangles.

  • 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


Question 4 if b 50 degrees and b 100 what is c l.jpg
Question 4: in right triangles. If B = 50 degrees and b = 100 what is c?

B

A. 155

c

________

B. 130

___________

a

________

A

C

C. 84

b


Nice try21 l.jpg
Nice try in right triangles.

  • What is the relationship between B and b? And, what is the relationship between b and c?

Return to question

Return to tutorial


Great job22 l.jpg
Great job! in right triangles.

  • 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


Introduction to quadrants l.jpg
Introduction to Quadrants in right triangles.

90 degrees

II

I

180 degrees______________________ 0 degrees

__________________

IV

III

270 degrees


Quadrants l.jpg
Quadrants in right triangles.

  • 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!


Importance of quadrants l.jpg
Importance of quadrants in right triangles.

  • 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”


All students take classes l.jpg
All Students Take Classes in right triangles.

  • 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


Standard angle values l.jpg
Standard Angle Values in right triangles.


Remember l.jpg
Remember in right triangles.

  • Simplify the fractions

  • Place the radicals in the numerator. Write

  • Instead of


Congratulations l.jpg
Congratulations in right triangles.

  • 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


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