MAC 1114 Topics (Lial 10th ed)
This page is one of the most important pages in this syllabus contains the main topic of the course. The only material/examples required to read is listed below.
Ch 1 Trigonometric Functions
Chapter 1 PowerPoint Examples’ Link
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1.1 Angles (Examples 1-6) (Video link)
1.2 Angle Relationship and Similar Triangles (Examples 1-5) (Video link)
1.3 Trigonometric Functions (Examples 1-4) (Video link)
1.4 Using the Definition of the Trigonometric Functions (Examples 1-7) (Video link)
You are required to memorize and know how to use the Reciprocal Identities in the shaded box on page 29, the Pythagorean Identities in the shaded box on page 33 and the Quotient Identities in the shaded box on page 34.
Note: To memorize, look for patterns. Once you know the values of the sine and the cosine functions, tangent =sine/cosine; cotangent =1/tangent; secant=1/cosine; and cosecant=1/sine.
Study the ‘Chapter 1 Test Prep’ starting on page 38 for sections 1.1-1.4.
Do the ‘Chapter 1 Test’ (problems 1-22) starting on page 43.
Ch 2 Acute Angles and Right Triangles
Chapter 2 PowerPoint Examples’ Link
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2.1 Trigonometric Functions of Acute Angles (Examples 1-3, 5 only) (Video link)
You are required to memorize and know how to use the Right Triangle-Based Definition of Trigonometric Functions in the shaded box on page 46, and the Cofunction Identities on Page 47
Note: These are the same definitions as the ones used on page 22. You only need to memorize the definition for Sine and Cosine. To find the rest of the functions, use the Reciprocal Identities on page 29 and the Quotient Identities on page 34.
2.2 Trigonometric Functions of Non-Acute Angles (Examples 1-4,6) (Video link)
You are required to know how to use (find) the exact value of the Trigonometric functions for Acute and non-Acute Special Angles without using the calculator. For an optional method to find trigonometric ratios of non-acute angles, refer to the Special Angles Degree link (click the link), (also in the Practice Problems section of the course documents.) You are required to memorize the table (see the pattern).
2.3 Finding Trigonometric Functions Values Using a Calculator (Examples 1-3) (Video link)
2.4 Solving Right Triangles (Examples 1-4) (Video link)
2.5 Further Applications of Right Triangles (Examples1,2,4) (Video link)
Study the ‘Chapter 2 Test Prep’ starting on page 86 for sections 2.1-2.5
Do the ‘Chapter 2 Test’ (problems 1-3 and 5-19) on page 92.
Only doing the practice test will not be enough to learn the material and pass the test.
This test is a two-part test; Calculator/ No-calculator
This concludes the material for TEST 1
Ch 3 Radian Measure and Circular Functions
Chapter 3 PowerPoint Examples’ Link
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3.1 Radian Measure (Examples 1-3) See the Angle Spectrum Link (Video link)
3.2 Application of Radian Measure (Examples 1-5) (Video link)
3.3 Skip this section.
3.4
Linear and Angular speed (Examples 1-3) (Video link)Linear and Angular speed extra problems
You are required to know how to use (find) the exact value of the Trigonometric functions for Acute and non-Acute Special Angles without using the calculator. For an optional method to find trigonometric ratios of non-acute angles, refer to the Special Angles Radians link (click the link). You are required to memorize that table (see the pattern).
Study the ‘Chapter 3 Test Prep’ on page 126 for sections 3.1,3.2,3.4
Do the ‘Chapter 3 Test’ (problems 1-14,18,19,20) starting on page 131.
Ch 4 Graphs of the Circular Functions
Chapter 4 PowerPoint Examples’ Link
If you do not have Power Point, go to PPT Get Power Point Viewer
4.1 Graphs of Sine and Cosine Functions (Examples 1-6) (Video Link)
4.2 Translations of Graphs of Sine and Cosine Functions (Examples 1-4) (Video Link)
Go to the link Trig graphs for examples on finding a function from its graph. You can check your answers by graphing it in the shown window.
4.3 Graphs of Tangent and Cotangent Functions (Examples 1-3,6) (Video Link)
4.4 Graphs of Secant and Cosecant Functions (Examples 1-3) (Video Link)
4.5
Harmonic Motion (Examples 1-2) (Video Link)You are required to memorize the graphs of the (Circular) Trigonometric Functions.
Study the ‘Chapter 4 Test Prep’ starting on page 181 for sections 4.1-4.5
Do the ‘Chapter 4 Test’ (problems 1-12, 14) starting on page 187.
Only doing the practice test will not be enough to learn the material and pass the test.
This test is a two-part test; Calculator/ No-calculator
This concludes the material for TEST 2
Ch 5 Trigonometric Identities
Chapter 5 PowerPoint Examples’ Link
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5.1 Fundamental Identities (Examples 1,3) (Video Link)
If you forgot the fundamental identities you learned in section 1.4, you are required to memorize and know how to use the Fundamental Identities in the shaded box on page 191.
5.3 Sum and Difference Identities for Cosine (Examples 1-5) (Video Link)
You are required to memorize and know how to use the 'Cosine of a Sum or Difference' formulas in the shaded box on page 206, but you are not required to know how to derive the formulas.
You are required to memorize and know the Cofunction Identities in the shaded box on page 207
5.4 Sum and Difference Identities for Sine and Tangent (Examples 1-3) (Video Link)
You are required to memorize and know how to use the 'Sine of a Sum or Difference' formulas and the ‘Tangent of a Sum or Difference’ formulas in the shaded boxes on page 216.
Note: To find formulas for tangent, you can divide the sine by the cosine.
5.5 Double-Angle Identities (Examples 1,2,4,5) (Video Link)
You are required to memorize and know how use the Double-Angle Identities in the shaded box on page 225.
5.6 Half-Angle Identities (Examples 1-4 only) (Video Link)
You are required to memorize and know how to use the half-Angle Identities in the shaded box on page 233.
Note: To find formulas for tangent, you do not need to memorize formulas. Just divide the sine by the cosine.
Study the ‘Chapter 5 Test Prep’ starting on page 240 for sections 5.1, 5.3-5.6
Do the ‘Chapter 5 Test’ (problems 1-9) starting on page 244.
Ch 6 Inverse Circular Functions and Trigonometric Equations
Chapter 6 PowerPoint Examples’ Link
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6.1 Inverse Circular Functions (Examples 1-7 only) (Video Link)
6.2 Trigonometric Equations I (Examples 1-3 only) (Video Link)
6.3 Trigonometric Equations II (Examples 1-3 only) (Video Link)
See the Identities and Inverse Functions Link
Study the ‘Chapter 6 Test Prep’ starting on page 282 for sections 6.1, 6.2, 6.3
Do the ‘Chapter 6 Test’ (problems 1-6) starting on page 287.
Only doing the practice test will not be enough to learn the material and pass the test.
This test is a No-calculator test
This concludes the material for TEST 3
Ch 7 Applications of Trigonometry and Vectors
Chapter 7 PowerPoint Examples’ Link
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7.1 Oblique Triangle and The Law of Sines (Examples 1-5) (Video Link)
You are required to memorize and know how use the Law of Sines.
7.2 Skip this section.
7.3 The Law of Cosines (Examples 1-5) (Video Link)
Skip the derivation of Heron’s formula
You are required to memorize and know how use the Law of Cosines.
Go to the link Laws of Sines and Cosines to learn how to use the laws with obtuse triangles
7.4 Vectors, Operations, and the Dot Product. (Examples 1-7) (Video Link)
7.5 Applications of Vectors (Example 1-5) (Video Link)
Study the ‘Chapter 1 Test Prep’ starting on page 340 for sections 7.1, 7.2, 7.4, 7.5
Do the ‘Summary Exercises on Applications of Trigonometry and Vectors’ (problems 1-10) starting on page 338.
Do the ‘Chapter 7 Test’ (problems 1-5, 9-11, 14-19) starting on page 347.
Ch 8 Complex Numbers, Polar Equations, and Parametric equations
Chapter 8 PowerPoint Examples’ Link
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8.5 Polar Equations and Graphs (Example 1-8) (Video Link)
Study the ‘Chapter 8 Test Prep’ starting on page 403 for section 8.5
Do the ‘Chapter 8 Test’ (problems 9-13) starting on page 406.
Only doing the practice test will not be enough to learn the material and pass the test.
This test is a two-part test; Calculator/ No-calculator
This concludes the material for TEST 4
Final Exam
Since the final exam will be comprehensive (cumulative), it will contain questions on the previously tested topics. Please check the Practice Tests 1, 2, 3 and 4 above.
The Final exam is a two-part test; Take-Home part and Testing-Center part.