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STANDARD COMPETENCIES: |
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a. |
Acquire an understanding of trigonometric vocabulary. Measure angles in degrees and radians. |
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b. |
Calculate the values of trigonometric functions of acute angles using right triangles. Evaluate trigonometric functions for general angles. Use reference angles to evaluate trigonometric functions. |
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c. |
Construct the graphs of the trigonometric functions. |
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d. |
Read and interpret angular and linear velocity type problems. |
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e. |
Read, interpret, and use drawing to solve survey type problems. |
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f. |
Recall and apply the reciprocal, quotient, Pythagorean, and even-odd identities to simplify expressions |
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g. |
Use the fundamental identities to verify trigonometric identities. |
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h. |
Employ the formulas for sums and differences to find the exact values of the trigonometric functions for selected angles, and to simplify expressions. |
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i. |
Derive and use the double-angle and half-angle formulas. |
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j. |
Use the product and sum formulas, and graph combination of sine and cosine functions. |
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k. |
Describe the relationship between the trigonometric functions and their inverses. |
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l. |
Calculate solutions for trigonometric equations with variable side conditions. |
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m. |
Solve right triangles. |
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n. |
Use the law of sines to solve a general triangle, including ambiguous case. |
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6. |
COURSE OUTLINE |
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1. Angles and the Trigonometric Functions |
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1.1 Angles and Degree Measure |
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1.2 Radian Measure, Arc Length, and Area |
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1.3 Angular and Linear Velocity |
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1.4 The Trigonometric Functions |
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1.5 The Fundamental Identity and Reference Angles |
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1.6 Right Triangle Trigonometry |
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2. Graphs of the Trigonometric Functions |
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2.1 Graphs of the Sine and Cosine Functions |
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2.2 The General Sine Wave |
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2.3 Graphs of the Tangent and Cotangent Functions |
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2.4 Graphs of the Secant and Cosecant Functions |
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2.5 Combining Functions |
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3. Trigonometric Identities |
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3.1 Basic Identities |
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3.2 Verifying Identities |
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3.3 Sum and Difference Identities for Cosines |
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3.4 Sum and Difference Identities for Sine and Tangent |
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3.5 Double-Angle and Half-Angle Identities |
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3.6 Product and Sum Identities |
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4. Solving Conditional Trigonometric Equations |
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4.1 The Inverse Trigonometric Functions |
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4.2 Basic Sine, Cosine, and Tangent Equations |
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4.3 Multiple Angle Equations |
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4.4 Trigonometric Equations of Quadratic Type |
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5. Applications of Trigonometry |
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5.1 The Law of Sines |
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5.2 The Law of Cosines |
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5.3 Area of a Triangle |
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5.4 Vectors
5.5 Applications of Vectors |