Trigonometry Unit Review PDF

UNIT E REVIEW: Trigonometry Name: _________________ 1 2 Outcome E1: Demonstrate an understanding of angles in standard position, expressed in degrees and radians. Multiple Choice 1. Consider the arc drawn on each circle. Which arc measure is closest to 3 radia...

UNIT E REVIEW: Trigonometry Name: _________________ 1 2 Outcome E1: Demonstrate an understanding of angles in standard position, expressed in degrees and radians. Multiple Choice 1. Consider the arc drawn on each circle. Which arc measure is closest to 3 radians? 2. Which of the following angles terminates in Quadrant III? 7 a. 3 radians b. radians c.  2100 d. 5000 5 Written Response 3. A student is using the formula s  r to find the arc length of a circle. Given a central angle measure of 350 and a radius of 6 cm, the student’s solution is as follows: s  356 s  210 cm Explain why this solution is incorrect. Write the correct solution. 3  7 4. Draw the angle  in standard position. 8 5. A central angle of a circle subtends an arc length of 5 cm. Given the circle has a radius of 9 cm, find the measure of the central angle in degrees. (calculator) 5 6. Angle θ, measuring , is drawn in standard position as shown below. 4 Determine the measures of all angles in the interval  4 , 2  that are coterminal with θ. 4 7. Determine one positive and one negative coterminal angle with the 5𝜋 angle. 6 27𝜋 8. Find the co-terminal angle to over the interval [-360°, 0°]. 5 9. Sketch the angle of 5 radians in standard position. 5  10. Use the information in the diagram to determine the value of arc length “s”. Outcome E2: Develop and apply the equation of the unit circle. 11. Determine the coordinate of the point (x, y) on the unit circle if you are given   30 0 where  is in standard position. 1 12. If the point ( , 𝑦) is on the unit circle, find 𝑦. 4 √5 −1 13. Verify if the point ( , ) lies on the unit circle. 2 2 6 14. For each of the following, find the exact value: 7 Outcome E3: Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees. 15. Given the point A(-3,5) on the terminal arm of an angle θ, identify the value of cotθ. 3 5 4 5 a. − b. − c. − d. − 5 3 5 4 16. Your classmate, Leo, was absent for one of his math lessons. Explain to Leo how to determine the cosecant ratio for an angle in standard position given that P(-3, -4) is a point on the terminal arm of the angle. 19  17. Explain how to find the exact value of sec .  6  8 18. The terminal arm of an angle  , in standard position, intersects the unit  5  circle in Quadrant IV at a point P , y . Determine the value of sin 𝜃.  4  19. Find the exact value of the following expression:  11   4   5  sin   sec   tan    3   3   6  11𝜋 11𝜋 20. Evaluate: (𝑠𝑖𝑛 ) (𝑠𝑒𝑐 ) 3 6 11𝜋 −3𝜋 23𝜋 21. Evaluate: csc ( 6 ) + 𝑠𝑖𝑛2 ( 4 ) + cos( 3 ) 9  3 22. If 𝜃 terminates in quadrant II and csc𝜃 = , determine the exact value 2 of tan𝜃. Outcome E4: Solve, algebraically and graphically, first- and second-degree trig equations with the domain expressed in degrees and radians. 23. Solve the following equation for 0 ≤ 𝜃 ≤ 360°. Express your answer in radians correct to 3 decimal places. 3 sin 2   14 sin   5  0 10 24. Solve the equation csc2   3 csc  4  0 over the interval 0, 2 . Express your answers as exact values or correct to 3 decimal places. 𝜋 25. Given the equation 2𝑠𝑖𝑛2 𝜃 − 3𝑠𝑖𝑛𝜃 + 1 = 0 verify that 𝜃 = is a 2 solution. 26. Solve the following equation over the interval 0 ≤ 𝜃 < 2𝜋. (𝑡𝑎𝑛𝜃 − 3)(𝑡𝑎𝑛𝜃 + 1) = 0 27. Solve, algebraically, sin 𝑥 (sec 𝑥 + 3) = 0 over the interval [−2𝜋, 𝜋] 11