Trig Final Exam
1. Simplify cosx +sinxcotx
cosxsinx - cosxcotx
0
2cosx
1
2. Which of the following expressions is
equal to 1-sec4θ ?
-2tan2θ -tan4θ
tan2θ -tan4θ
2tan2θ -tan4θ
-2tan2θ +tan4θ
3. Simplify:
-2cotxcscx
2sec2x
-2tanxsecx
2csc2x
4. Simplify
cot2x -1
cot2x +1
cannot be simplified
1-cot2x
5. Simplify (tanx-secx)(tanx+secx)
1
-1
0
sec2x -tan2x
6. Solve for all values of x:
7 - 6sinx = 3 + 2sinx
120ο
180ο
135ο
150ο or 30ο
8. Solve for x in [0,2π) :
cot2x +2 =2cscx
3π/2
0, π
π/2, 3π/2
π/2
9. Solve: 2 cot2x - 4= 2
π/6 + nπ/2; 5π/6 + nπ/2
π/6 + nπ; 5π/6 + nπ
π/3 + nπ; 2π/3 + nπ
π/6 + 2nπ; 7π/6 + 2nπ
10. Solve for x in [0, 2π): cotxsinx + cotx =0
0 ; 3π/2
0; π/2
π/2
∏∕2, 3π/2
11. Find the exact value of
Tan(155
+ tans(-95 )
1-tan(155 tan(-95 )
1/
-
/3
12. Find the exact value of cos15 .
/4
13. Find the magnitude of the horizontal
and vertical components of a velocity
of 630 mph flying in the direction S20
horizontal: 215mph, vertical: 6mph
horizontal: -222 mph, vertical: 592mph
horizontal: -422mph, vertical: -380mph
horizontal: -215mph, vertical: -592mph
14. A commercial passenger jet is flying with
an airspeed of 135 knots on a bearing
of N45οE. If a 32-knot wind is blowing
at a bearing of S79οE,
determine the velocity and direction
of the jet relative to the ground.
120.1 knots, S55οE
129.2 knots, S35οE
155.2 knots, N55οE
155.2 knots, N35οE
15. Given vectors
u=<-2,3> and v=<-2,3>, find 9u -5v
<7,9>
<13,9>
<-8,12>
<-5,9>
16. Find the direction angle of 13i + 15j.
56.65ο
229.09ο
139.09ο
49.09ο
17. An airplane is traveling due east with a
velocity of 563mph. The wind blows at
76mph at an angle of S43οE.
What is the resultant speed and direction
of the plane?
617.3mph, S84.8οE
617.3mph, S5.2οE
620mph, S9.5οE
620.3mph, S85.2οE
18. Find one set of polar coordinates for
(-5, 5√3)
(10, 2π/3)
(5, 2π/3)
(2π/3, 10)
(-10, 2π/3)
19. Find the rectangular coordinates of
(7, 30ο)
(-6.06, -3.5)
(6.06, -3.5)
(6.06, 3.5)
20. How many triangles are there that satisfy
the conditions a=13, b=6 and A =61ο?
0
2
not possible
1
21. Given a triangle with a=14, A=41ο, and B=34ο
What is the length of c?
21.6
20.6
19.6
22.6
22. What is the length of a?
Given a triangle with
b=7, c=9 and A=36ο
5.3
28.1
14.1
10.6
23. Find the area of the triangle with
a=15ft, b=22ft and C=30ο.
142.9
82.2
165
285.8
24. Find the area of the triangle with
a=10ft, b=4ft and c=12ft.
15.7
18.7
20.7
19.7
25. Find the trigonometric form of the complex number z = -2 - 2
6cis(210
4cis(240
-4cis(240
8cis(120
26. Name the polar coordinates of the point graphed.
(4, π/3)
(5, π/4)
(5, π/3)
(4, π/4)
i