Inverse Trigonometry
For1‐10,evaluateeachexpression.Leaveyouranswerindegrees.
1. sin
1

2
2
3
2
2. arc cos
4. sec
2
)
2
6. cot (sin 90) 3. cot
1
0
5. cos(cos
1
1
2
1
8. arc tan(sin 0) 7. tan(c sc (  2)) Evaluatetheexpression.Leaveyouranswerinradians.
1

2
1
s
in


 9.
 2 
1

2
10. arccos 
 2 
arc
csc
12.

 3

13. arc sec  2  14. arc cot1 16. tan( sec
1
11. tan 0 15. cos (sin  ) 1
1
2) Evaluateeachexpression.
12
17. sin(tan 1 ) 5
1 5
) 19. csc( sec
4
21.Solve: 2cos2 x  cos x  1
23.Solve: 4cos2  2x   1  0
2
5
18. cos(arc sin ) 7
20. cot( arc cos ) 9
 2 ,2  22.Solve: tan sec  2tan
 90,90  allsolutions
24.Writetheparticularequationofthegraph. 25.Writetheparticularequationofthegraph.






















26.Sketchfullcyclesof:(nocalc)


a. y  2cos  x  3   3 4

3 
b. y  3 tan  x  +1
2 
c. y  4  csc 3  60 Solveallfor
26 secx 1 0for x є [0, 2]27 4sin2   11sin  3
x є [-180°, 180°]
28) 4cos²x 8  9 for x є [0, 2]29) 2cos3θ–1 0.xє ‐180°,180°
30 2cot²θ‐cotθ‐1 0xє 0°,180° 31 tanx sinx –sinx 0
all solutions 32 2cos²x 3sinx  0 x є [-, ]33 13 cos x  3  0 x є [0, 360°]
34.WhileacontestantonFearFactor,yourtaskistobeattachedtothesideofalargespinningwheelwhereyou
mustfindthecorrectkeyinordertomakethewheelstop.Unfortunately,partofthewheelisunderwateratall
times.Thediameterofthewheelis30feet,themaximumheightobtainedis25feetandittakes12secondsforone
revolution.Whilespinningaroundonthewheel,tryingtoholddownallofthepiginnersyouateinthelast
competition,yourealizethatyourdistanceabovethewatervariessinusoidallywithtime.Afterspinninginthe
wheelfor3seconds,youareatthemaximumheight.
a.Sketchthegraphofthisfunction.
b.Writetheequationofthesinusoid.c.Listthefirstthreetimesyouareataheightof21feet.