MA 15400 Spring 2011 Exam 1 PYTHAGOREAN IDENTITIES sin2θ+cos2θ=1 1+tan2θ=sec2θ 1+cot2θ=csc2θMA 15400 Exam 1 Spring 2011 Covers Lessons 1 to 11, which include all of Sections 6.1, 6.2, 6.3, 6.4, and 6.5 1 1. Which of the following are not coterminal angles with 150θ= − °? A. 5 17,6 6π π B. 210 , 510° − ° C. 17 31,6 6π π− D. 930 , 870° − ° E. All of the above are coterminal angles. 2. Find the complementary angle to 17 4' 12"θ= °. A. "40'18162° B. "48'5572° C. "40'1872° D. "48'55162° E. None of the above. 3. Find the area of the sector of the circle with radius 7.9 cm, whose central angle θ subtends an arc of 5.6 cm. Round your answer to one decimal place. A. 21.31 cm B. 21.62 cm C. 21.11 cm D. 21.22 cm E. None of the above.MA 15400 Exam 1 Spring 2011 Covers Lessons 1 to 11, which include all of Sections 6.1, 6.2, 6.3, 6.4, and 6.5 2 4. A pendulum in a grandfather clock is 5 feet long and swings back and forth along an 8 inch arc. Approximate the angle, to the nearest tenth of a degree, through which the pendulum passes during one swing. (12 inches = 1 foot) A. °8.6 B. °5.7 C. °7.6 D. °6.7 E. None of the above. 5. Stonehenge was constructed using solid stone blocks weighting over 99,000 pounds each. Lifting a single stone required 550 people, who pulled the stone up a ramp inclined at an angle of °9 . Approximate the distance the stone was moved along the ramp in order to raise it to a height of 40 feet? Round your answer to the nearest foot. A. feet256 B. feet157 C. feet213 D. feet194 E. None of the above. 6. Approximate to four decimal places. ()°159cot A. 0711.1− B. 0001.0 C. 7904.2 D. 6051.2− E. None of the above.MA 15400 Exam 1 Spring 2011 Covers Lessons 1 to 11, which include all of Sections 6.1, 6.2, 6.3, 6.4, and 6.5 3 7. Which of the following is equivalent to: ()θθθ222cscseccos + A. θ2sec B. θ2tan C. θ2csc D. θ2sin E. θ2cot 8. Find the exact value of θcos, if θis in standard position and the terminal side of θ is in QIIand parallel to the line 1247=+yx. A. 657 B. 654− C. 657− D. 654 E. None of the above. 9. Which of the following is equivalent to: ()( )xx−−cossin A. xtan− B. θcot− C. xtan D. θcot E. xcscMA 15400 Exam 1 Spring 2011 Covers Lessons 1 to 11, which include all of Sections 6.1, 6.2, 6.3, 6.4, and 6.5 4 10. Let ()tP be the point that the terminal side of the angle t intersects the unit circle. If ( )−−=257,2524tP , find ()tP−. A. −−257,2524 B. −257,2524 C. −257,2524 D. 257,2524 E. None of the above. 11. As ( )__________tan,23→→+xxπ A. undefined B. ∞− C. 0 D. ∞ E. 1 12. Find the exact value of 34cscπ. A. 32 B. 2 C. 2− D. 32− E. None of the aboveMA 15400 Exam 1 Spring 2011 Covers Lessons 1 to 11, which include all of Sections 6.1, 6.2, 6.3, 6.4, and 6.5 5 13. Approximate to the nearest 01.0radians, all angles θ in the interval [)π2,0 that satisfy the equation: 4682.1sec=θ A. 96.3,32.2 B. 96.3,82.0 C. 46.5,32.2 D. 46.5,82.0 E. None of the above 14. Find the period and phase shift of the following function. 1 35sin4 4y xπ = − A. , 32Period Phase Shiftππ= = B. 8 , 3Period Phase Shiftπ π= = C. 3,2 16Period Phase Shiftπ π= = D. 38 ,16Period Phase Shiftππ= = E. None of the aboveMA 15400 Exam 1 Spring 2011 Covers Lessons 1 to 11, which include all of Sections 6.1, 6.2, 6.3, 6.4, and 6.5 615. Find the graph of the function3sin 24y xπ = + . A B C D 4π π 4π− π− 4π π 4π− π− 4π π 4π− π− 4π π 4π−
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