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# Trig m1 handouts

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### Trig m1 handouts

1. 1. MAC 1114 Module 1 Trigonometric FunctionsRev.S08 Learning ObjectivesUpon completing this module, you should be able to:1. Use basic terms associated with angles.2. Find measures of complementary and supplementary angles.3. Calculate with degrees, minutes, and seconds.4. Convert between decimal degrees and degrees, minutes, and seconds.5. Identify the characteristics of an angle in standard position.6. Find measures of coterminal angles.7. Find angle measures by using geometric properties.8. Apply the angle sum of a triangle property. http://faculty.valenciacc.edu/ashaw/Rev.S08 Click link to download other modules. 2 Learning Objectives (Cont.) 9. Find angle measures and side lengths in similar triangles. 10. Solve applications involving similar triangles. 11. Learn basic concepts about trigonometric functions. 12. Find function values of an angle or quadrantal angles. 13. Decide whether a value is in the range of a trigonometric function 14. Use the reciprocal, Pythagorean and quotient identities. 15. Identify the quadrant of an angle. 16. Find other function values given one value and the quadrant. http://faculty.valenciacc.edu/ashaw/Rev.S08 Click link to download other modules. 3 1
2. 2. Trigonometric Functions There are four major topics in this module: - Angles - Angle Relationships and Similar Triangles - Trigonometric Functions - Using the Definitions of the Trigonometric Functions http://faculty.valenciacc.edu/ashaw/ Rev.S08 Click link to download other modules. 4 What are the basic terms?  Two distinct points determine a line called line AB. A B  Line segment AB—a portion of the line between A and B, including points A and B. A B  Ray AB—portion of line AB that starts at A and continues through B, and on past B. A B http://faculty.valenciacc.edu/ashaw/ Rev.S08 Click link to download other modules. 5 What are the basic terms? (cont.) Angle-formed by rotating a ray around its endpoint. The ray in its initial position is called the initial side of the angle. The ray in its location after the rotation is the terminal side of the angle. http://faculty.valenciacc.edu/ashaw/ Rev.S08 Click link to download other modules. 6 2
3. 3. How to Identify a Positive Angle and a Negative Angle?  Positive angle: The  Negative angle: The rotation of the terminal rotation of the terminal side of an angle side is clockwise. counterclockwise. http://faculty.valenciacc.edu/ashaw/ Rev.S08 Click link to download other modules. 7 Most Common unit and Types of Angles The most common unit for measuring angles is the degree. The major types of angles are acute angle, right angle, obtuse angle and straight angle. http://faculty.valenciacc.edu/ashaw/ Rev.S08 Click link to download other modules. 8 What are Complementary Angles? When the two angles form a right angle, they are complementary angles. Thus, we can find the k +20 measure of each angle in this k − 16 case. The two angles have measures of 43 + 20 = 63° and 43 − 16 = 27° http://faculty.valenciacc.edu/ashaw/ Rev.S08 Click link to download other modules. 9 3
4. 4. What are Supplementary Angles?  When the two angles form a straight angle, they are supplementary angles. Thus, we can find the measure of each angle in this case too. 6x + 7 3x + 2 These angle measures are 6(19) + 7 = 121° and 3(19) + 2 = 59° http://faculty.valenciacc.edu/ashaw/ Rev.S08 Click link to download other modules. 10 How to Convert a Degree to Minute or Second?  One minute is 1/60 of a degree.  One second is 1/60 of a minute. http://faculty.valenciacc.edu/ashaw/ Rev.S08 Click link to download other modules. 11 Example Perform the calculation.  Perform the calculation.  Write Since 86 = 60 + 26, the sum is written http://faculty.valenciacc.edu/ashaw/ Rev.S08 Click link to download other modules. 12 4