Presentation on theme: "Introduction to Trigonometric Functions"— Presentation transcript:
1Introduction to Trigonometric Functions Return to home page
2Trig 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,
3You 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.
4How does this relate to trig? The opposite side divided by the hypotenuse, a/c, is called the sine of angle AThe adjacent side divided by the hypotenuse, b/c, is called the cosine of Angle AThe opposite side divided by the adjacent side, a/b, is called the tangent of Angle A
5Remember SOHCAHTOA Sine is Opposite divided by Hypotenuse Cosine is Adjacent divided by HypotenuseTangent is Opposite divided by AdjacentSOHCAHTOA!!!!!!
6Table of ContentsExamplesQuestion 1Question 2Question 3Question 4
7Example 1 If a = 3 and c = 6, what is the measurement of angle A?
8Answer: 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.
9Example 2A 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?
10How 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 relationshipLet x be the height of the flagpoleFrom your calculator, the tangent of 25 is .47.47 =x = (.47)(100), x = 47The flagpole is 47 feet high.
11Question 1 Given Angle A is 35 degrees, and b = 50 feet. Find c. Click on the correct answer.A. 61 feetB 87 feetC. 71 feet
12GREAT 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 61Next question
13Nice tryYou have an angle and the adjacent side. You want to find the hypotenuse.What relationship uses the adjacent and the hypotenuse?Back toQuestionBack to tutorial
14Question 2If the adjacent side is 50, and the hypotenuse is 100, what is the angle? Please click on the correct answer.A. 60 degreesB. 30 degreesC. 26 degrees
15Way 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 degreesNext question
16Nice tryGiven an adjacent side and a hypotenuse, what relationship will give you the angle?Back to questionBack to tutorial
17Question 3If the opposite side is 75, and the angle is 80 degrees, how long is the adjacent side?A. 431B. 76C. 13
18Nice jobYou 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 = = 13Next question
19Nice TryYou 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 questionBack to tutorial
20Question 4: If B = 50 degrees and b = 100 what is c? ________B. 130___________a________AC. 84Cb
21Nice tryWhat is the relationship between B and b? And, what is the relationship between b and c?Return to questionReturn to tutorial
22Great 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
23Introduction to Quadrants 90 degreesIII180 degrees______________________ 0 degrees__________________IVIII270 degrees
24Quadrants All angles are divided into 4 quadrants Angles between 0 and 90 degrees are in quadrant 1Angles between 90 and 180 degrees are in quadrant IIAngles between 180 and 270 degrees are in quadrant IIIAngles between 270 and 360 degrees are in quadrant IVWhy is this important? Click and find out!
25Importance 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”
26All Students Take Classes Quadrant I: 0 – 90 degrees: All: All trig functions are positiveQuadrant II: 90 – 180 degrees: Students: Sine functions are positiveQuadrant III: 180 – 270 degrees: Take: Tangent functions are positiveQuadrant IV: 270 – 360 degrees: Classes; Cosine functions are positive
28Remember Simplify the fractions Place the radicals in the numerator. WriteInstead of
29CongratulationsYou 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