Name ____________________________
Pre-calculus Honors/GT
Date ________________Period ________
Special Angle Worksheet
I.
Complete the table below: (Use exact values only, NO DECIMALS)
0 ≤ θ < 2π
Angle
sinθ
cosθ
tanθ
cscθ
secθ
1
3
2
2√3/3
cotθ
(in radians)
1. π/6
2. 3π/4
3. 3π/2
4. 2π/3
1
2
√2/2
√3/2
−1
2
-1
0
Undefined
−1
undefined
-1/2
− 3
2√3/3
−2
-√2/2
1
− 2
-1
√3/2
5. 5π/4
-√2/2
6. 11π/6
-1/2
3
2
0
-1
0
1
7. π
5π
4
-√2/2
-√2/2
9. 11π/6
-1/2
√3/2
10. π/3
3
2
8.
1/2
√2
√3
−1
-√2
-√3/3
-√3/3
√3
-2
-√3/3
-√2
1
− 3
2√3/3
−1
undefined
-√2
0
undefined
-√2
−2
2√3/3
1
2√3/3
− 3
2
1
3
II. Evaluate each of the following using a calculator: (Round answers to 4 decimal places)
11.
⎛ 21π ⎞
2
4sec (420° ) − tan ⎜ −
⎟ + 6sin (49°10ʹ )=
4 ⎠
11.4963
⎝
12.
1 2 ⎛ 11π ⎞
⎛ ⎛ π ⎞⎞
cot ⎜ −
⎟ + 2 (sin (20° ) )⎜ csc ⎜ − ⎟ ⎟ =
2
3 ⎠
⎝
⎝ ⎝ 6 ⎠⎠
-1.2014
13.
⎛ sin (40° ) ⎞
3π ⎞
2⎛
sec (4.89 ) − 10 ⎜⎜
⎟⎟ + 5 tan ⎜ −
⎟=
4 ⎠
⎝
⎝ cos (70° ) ⎠
-8.1339
14.
7π ⎞
5π ⎞
⎛
2⎛
cot (66°10ʹ ) − 5 ⎜ sin
⎟ + csc ⎜ −
⎟=
3 ⎠
4 ⎠ -1.7578
⎝
⎝
15.
⎛ 12π ⎞
sin (90° − 42°12ʹ ) + cos ⎜
⎟=
⎝ 5 ⎠
1.7452