READ DIRECTIONS CAREFULLY

Directions: Solve each equation and write the general equation for all possible solutions using radians. (4pts) 1. 4 cos x = - 1 + 2 cos x 2. 3 cot 2 x = 1 Directions: Using factoring, solve the equations for all solutions on the interval [0, 27). (4pts each) 3. 4 sin2 x - 4 sin x = -1 4. 2 sin x cos x = -cos x Directions: Prove the following identities. (3 pts each) 5. (cscx - tan x) sin x cos x = cos x - sin2x sin2x+cos2x+cot2x _ 6. = cotz x tan2x+1Directions: Using factoring and trigonometric identities, simplify the following expressions. (2 pts) 7. tan2 0 sec 0 + 1 Read all directions carefully regarding vectors and which form to use. 8. Given: Write the vector that initiates on (-3, 6) and terminates on (8, 2) in component form. (2 pts) 9. Given: The boat that travels 45 mph, in a direction 50 west of North. Write the vector in component form. (2pts) 10. Given: u = (4, 7) and w = (5, -8), find 3u - 2w and leave your answer in component form. (2 pts) 11. A child pulls a wagon with a force of 40 pounds. The handle makes an angle of 30 with the ground. Express the force vector in component form. (2 pts) 12. A plane is flying due northwest at an airspeed of 550 mph. a.) Resolve the flight path into the vertical and horizontal components. Leave your answer in component form. (2 pts) b.) There is a 25 mile per hour wind blowing from the north (2709). How many degrees off course will the plane end up flying and what is the plane's groundspeed? (3 pts) 13. Nathaniel is hiking in the woods. He travels 40 north of east for 3 miles, then he turns and walks 30 east of south for 5 miles, and finally he travels straight west for 3 miles. How far is he from his starting position? In what direction will he need to walk to travel to get back? (4 pts)14. Jacob and Brendan are pulling on Matt to keep him from running out of this math test. While John stands in the hallway and laughs at Matt. Jacob and Brendan pull with forces of 20 pounds and 28 lbs at the angles shown in the figure. How hard is Matt pulling back if he is holding Jacob and Brendan at a standstill (equilibrium)? (4 pts) 20 lbs 15 3 28 lbs Pythagorean Identities sin? 0 + cos? 0 =1 tan? 0 + 1 = sec? 6 cot? 0 + 1 = csc2 0 Cofunction Identities Even-Odd Identities sin 8 = cos -8 cose = sin # -8 sin(-0) = -sino csc (-8) =-csco csco = sec 5-8 sec 8 = csc -8 cos(-8) = Cose sec(-0) = sece tan 8 = cot 1- 0 cote = tan -0 tan (-0) =-tane cot(-8) =-cote