TAKE-HOME EXAM 3

MATH119PRE-CALCULUS WITH TRIGONOMETRYNAME:ID#:TAKE-HOME EXAM 3Solve the following problems showing all your work for full credit.1. (1 pt.) Find the distance between the points ( − 4, −7)and ( − 8, −5).2. (4 pts.) Find the point on the line y = 2x− 3 in the xy -plane that is closest to thepoint ( 5,1).3. (2 pts.) Find the equation of the circle in the xy -plane centered at (− 4,5)with radius6.224. (5 pts.) For the circle in the xy -plane described by the equation x + 5x+ y − 6y= 3find the center, radius and circumference.5. Find the endpoint of the radius of the unit circle that makes the given angle with thepositive horizontal axis.oa) (2 pts.) − 60 =b) (2 pts.)o135 =6. Find the angle the radius of the unit circle ending at the given point makes with thepositive horizontal axis. Among the infinitely many possible correct solutions, choosethe one with the smallest absolute value.⎛ 1 3 ⎞a) (2 pts.) ⎜ ⎟,− ⎝ 2 2 ⎠b) (2 pts.)⎛ 2 ⎞⎜ ⎟− ,⎝ 2 22⎠

7. Convert the angle θoa) (1 pt.) θ = 750 to radian measure in terms of π ;7πb) (1 pt.) θ = − to degree measure.98. (4 pts.) Find the distance along an arc on the surface of the earth that subtends a1central angle of 1minute(1minute = degree). This distance is called a nautical60mile . (The radius of the earth is 3960 mi.)9. Find the exact function value, if it exists:oa) (2 pt.) cos 2190 =ob) (2 pt.) cot( − 240 ) =c) (2 pt.)15π sin =4d) (2 pt.)22π tan =310. (1 pt.) Find the exact acute angle θ , in degrees, for which3cos θ = .2111. (10 pts.) Given that sinθ = − and that the terminal side is in quadrant III, find the7other five trigonometric function values.

12. Consider a triangle ABC with sides a , b and c and corresponding angles α , β andγ , withoγ = 90 .a) (5 pts.) If a = 4 3 and c = 8 find b , sin α , cos α , tanαand cot α .b) (3 pts.) If1cos α = find sin α , tanαand cot α .513. (5 pts.) The Eiffel Tower. When the top of the Eiffel Tower is viewed at a distanceoof 200 feet from the base, the angle of elevation is 79 .2 . Estimate the height of thetower.π14. If sin =8a) (4 pts.)2 − 2find217π cos .8b) (4 pts.)9sin π8c) (6 pts.)3tan π8

⎛ π ⎞15. Suppose α is in the interval ⎜ ,π ⎟ and tanα = −2find⎝ 2 ⎠a) (3 pts.) cos( − α)b) (3 pts.) sin( α − 7π)c) (3 pts.) tan ( α + 3π )16. Evaluatea) (1 pt.)cos −122b) (1 pt.)1sin −12−c) (1 pt.) tan 1 ( − 3)17. Suppose t is such thata) (2 pts.) cos −1 t2πsin −1t = − . Evaluate7−1b) (2 pts.) sin ( − t)18. Evaluate− ⎛ 1 ⎞a) (4 pts.) cos 1⎜cos⎟⎝ 2 ⎠⎛ −12 ⎞b) (4 pts.) cos⎜sin⎟⎝ 5 ⎠( )c) (4 pts.) sin tan−1 ( − 9)