trig_m2_handouts

trig_m2_handouts - MAC 1114 Module 2 Acute Angles and Right...

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1 Rev.S08 MAC 1114 Module 2 Acute Angles and Right Triangles 2 Rev.S08 Learning Objectives Upon completing this module, you should be able to: 1. Express the trigonometric ratios in terms of the sides of the triangle given a right triangle. 2. Apply right triangle trigonometry to find function values of an acute angle. 3. Solve equations using the cofunction identities. 4. Find trigonometric function values of special angles. 5. Find reference angles. 6. Find trigonometric function values of non-acute angles using reference angles. 7. Evaluate an expression with function values of special angles. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. 3 Rev.S08 Learning Objectives (Cont.) 8. Use coterminal angles to find function values . 9. Find angle measures given an interval and a function value. 10. Find function values with a calculator. 11. Use inverse trigonometric functions to find angles. 12. Solve a right triangle given an angle and a side. 13. Solve a right triangle given two sides. 14. Solve applied trigonometry problems. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
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2 4 Rev.S08 Acute Angles and Right Triangles http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. - Trigonometric Functions of Acute Angles - Trigonometric Functions of Non-Acute Angles - Finding Trigonometric Function Values Using a Calculator - Finding Trigonometric Function Values Using a Calculator - Solving Right Triangles There are four major topics in this module: 5 Rev.S08 What are the Right-Triangle Based Definitions of Trigonometric Functions? http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. For any acute angle A in standard position . Tip: Use the mnemonic sohcahtoa to remember that “sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.” 6 Rev.S08 Example of Finding Function Values of an Acute Angle http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Find the values of sin A , cos A , and tan A in the right triangle shown. A C B 52 48 20
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3 7 Rev.S08 Cofunction Identities http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. For any acute angle A , sin A = cos(90 ° A ) csc A = sec(90 ° A ) tan A = cot(90 ° A ) cos A = sin(90 ° A ) sec A = csc(90 ° A ) cot A = tan(90 ° A ) 8 Rev.S08 Example of Writing Functions in Terms of Cofunctions http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Write each function in terms of its cofunction . a) cos 38 ° cos 38 ° = sin (90 ° 38 ° ) = sin 52 ° b) sec 78 ° sec 78 ° = csc (90 ° 78 ° ) = csc 12 ° 9 Rev.S08 Example of Solving Trigonometric Equations Using the Cofunction Identities http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
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