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Name: _____________________________________________________ Period: ________ Date: ___________________ Group members: ____________________________________________________________________________________ Honors Pre-Calculus 2012-13 Ms. York Chapter 4 Test Review Directions: Below are questions that will help you prepare for the Chapter 4 Test. There will be a calculator part and a noncalculator part for the test. Try to complete the exercises without a calculator where it states “No Graphing Calculator.” Some formulas/definitions/identities that will be really helpful: radians arc length r time t central angle Angular Speed: time t 1 Area of a Sector of a Circle: A r 2 2 1 sec 1 sec cos 1 sin csc 1 csc sin sin tan cos cos cot sin x cos y sin 30-60-90 Triangle 45-45-90 Triangle Convert degrees to radians: multiply by 180 180 Convert radians to degrees: multiply by radians Arc Length: s r Linear Speed: v cos Section 4.1 – Radian and Degree Measure (No Graphing Calculator) 1. Convert 150 from degrees to radians and sketch the angle. 2. Convert 9 from radian to degrees and sketch the angle. 4 Section 4.2 – Trigonometric Functions: The Unit Circle (No Graphing Calculator) 3. Find the exact values of the six trigonometric functions when a. 2 sin 2 cos 2 1 1 tan 2 sec 2 1 cot 2 csc 2 Amplitude = a 2 Period = b Phase Shift: Left: bx c 0 Right: bx c 2 Vertical Shift: d b. 4 3 c. 7 4 Section 4.3 – Right Triangle Trigonometry (No Graphing Calculator) 4. Find the exact values of the six trigonometric functions given the triangle. sin __________________________ cos __________________________ tan __________________________ csc __________________________ sec __________________________ cot __________________________ 5. Use trigonometric identities to transform the left side of the equation into the right side. ( 0 tan cot csc 2 tan 2 ) Section 4.4 – Trigonometric Functions of Any Angle (No Graphing Calculator) 6. Find the exact value of a. tan 3 5 b. tan 6 5 c. sec 4 7. Find the exact values of the other five trigonometric functions given sin 1 and cos 0 . 2 cos __________________________ tan __________________________ csc __________________________ sec __________________________ cot __________________________ Section 4.5 – Graphs of Sine and Cosine Functions (No Graphing Calculator) 8. Graph y sin . Determine its domain, range, amplitude, and period. Domain: Range: Amplitude: Period: 9. Graph y cos . Determine its domain, range, amplitude, and period. Domain: Range: Amplitude: Period: Section 4.6 – Graphs of Other Trigonometric Functions (No Graphing Calculator) 10. Graph y csc . Determine its domain, range, amplitude, and period. Domain: Range: Amplitude: Period: 11. Graph y sec . Determine its domain, range, amplitude, and period. Domain: Range: Amplitude: Period: 12. Graph y tan . Determine its domain, range, amplitude, and period. Domain: Range: Amplitude: Period: 13. Graph y cot . Determine its domain, range, amplitude, and period. Domain: Range: Amplitude: Period: Section 4.7 – Inverse Trigonometric Functions (No Graphing Calculator) 14. Evaluate the expression. Keep your answer in radians. 3 a. arccos 2 b. arcsin(1) 15. Find the exact value of the expression. Keep answer in radians and rationalize if applicable. 1 a. sin arcsin 2 3 b. arcsin sin 4 c. 12 cot arcsin 13 16. Write an algebraic expression that his equivalent to (you do not need to rationalize) x a. tan arccos 2 b. sec(arcsin(x 1)) Section 4.8 – Applications and Models (Graphing Calculator Allowed) 17. An engineer erects a 75-foot cellular telephone tower. Find the angle of elevation to the tope of the tower at a point on the level ground 50 feet from its base. Find the angle measure to the nearest tenth of degree.