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**Introduction to Trigonometric Functions**

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**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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**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.

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**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

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**Remember SOHCAHTOA Sine is Opposite divided by Hypotenuse**

Cosine is Adjacent divided by Hypotenuse Tangent is Opposite divided by Adjacent SOHCAHTOA!!!!!!

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

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

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**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.

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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?

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**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.

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**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

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**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

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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

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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

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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

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

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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

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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

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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

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**Question 4: If B = 50 degrees and b = 100 what is c?**

________ B. 130 ___________ a ________ A C. 84 C b

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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

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**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

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**Introduction to Quadrants**

90 degrees II I 180 degrees______________________ 0 degrees __________________ IV III 270 degrees

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**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!

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**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”

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**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

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Standard Angle Values Angle 30 45 60 90 Sine Cosine Tangent

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**Remember Simplify the fractions**

Place the radicals in the numerator. Write Instead of

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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

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Objective: Students will be able to… Use the sine, cosine, and tangent ratios to determine missing side lengths and angle measures in a right triangle.

Objective: Students will be able to… Use the sine, cosine, and tangent ratios to determine missing side lengths and angle measures in a right triangle.

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