Download Practice Exam 1 - Plane Trigonometry | MATH 111 and more Exams Trigonometry in PDF only on Docsity! Math 111 - Trigonometry Practice Exam 1 Warning: This study guide is not all inclusive- there may be material on the test which is covered in the book but not here. This is simply meant to serve as a supplement to the problems in the book. 1. Find the angle of smallest positive measure co-terminal with each angle. (a) θ = −442◦ 278◦ (b) θ = 1826◦ 26◦ (c) θ = 688◦ 328◦ 2. Sketch each angle in standard position, and give the quadrant of each angle. (a) θ = −442◦ - Quadrant IV (b) θ = 688◦ - Quadrant IV 3. What are the defining characteristics of an isosceles, obtuse triangle? The triangle has two equal sides and one angle that is greater than 90 degrees. (b) sin(210 ◦) = −1/2 (c) csc(1110 ◦) = 2 (d) tan(−675 ◦) = 1 (e) cos(−330 ◦) = √ 3/2 8. Simplify the following expression: cos(120 ◦) + 2 sin2(60 ◦)− tan2(30 ◦) Using the double angle identity cos(2A) = 1− sin2A, we have cos(120◦) + 1− cos(120◦)− tan2(30◦) = 1− tan(30◦) Since sin 30◦ = 1 2 , cos(30◦) = √ 3 2 , we have tan(30◦) = 1√ 3 , so the expression is 1− tan2(30◦) = 1− 1 3 = 2 3 9. An 8 foot tall fire truck is parked 10 feet next to a 45 foot tall building. There is a man on the top of the building who is stranded, and the firefighters need to extend their 40 foot long ladder, located on top of the firetruck, to the roof to save the man. Is the ladder long enough to reach him? Why or why not? Our guess is that the author of this problem is not overly morbid and that the man does have a shot at survival. This should boil down to using Pythagorean Theorem on a triangle with legs of length 10 feet, and 37 feet. The hypotenuse is then √ 372 + 102 ≈ 38.33 feet, so the ladder can reach the top. 10. Convert the following from radians to degrees: (a) π/2 = 90◦ (b) 430 = 77400 π ◦ (c) 5π/7 = 900 7 ◦ (d) 2 = 360 π ◦ (e) 3π/4 = 135◦ (f) 12π = 2160◦ (g) 1000 = 180,000 π ◦ 11. Convert the following from degrees to radians: (a) 225◦ = 5 4 π (b) 430◦ = 43 18 π (c) 737◦ = 737 180 π (d) 2π◦ = π 2 90 (e) 3π/4◦ = π 2 240 (f) 720◦ = 4π (g) −1000◦ = −50 9 π (h) −547◦ = 547 180 π
