SOLUTION: 5: For questions 5 – 14: Solve each of the following for y in radians. Use a calculator for exercises 9 and 10, with 3.1416 as an approximation for π.
y = arctan 1
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Question 145209: 5: For questions 5 – 14: Solve each of the following for y in radians. Use a calculator for exercises 9 and 10, with 3.1416 as an approximation for π.
y = arctan 1
π/7
π/4
2π/5
2π/2
6: y = arcsin (sqrt 2)/2
π/4
4π/2
sqrt π
sqrt(4π)
7: y = arccot (-sqrt 3)/3
2/3π
-π
2π/3
π/9
8: y = arcos (-sqrt 3)/2
-6π
-3π/2
π/2
5π/6
9: y = arccot 1.804
.5062
.6
.4708
5.6
10: y = arccos -.3090
1.914
1.252
1.8849
.889
11: y = tan (arcsin -3/5)
4/3
3/5
-2/3
-3/4
12: y = cos (arccot 12/5)
-12/5
12/13
-4
¾
13: y = sin (arccos 2/3 + arctan 1)
(sqrt 10 + 2sqrt2)/6
10 + sqrt 2
6/(10 + 2sqrt2)
(sqrt 10 + sqrt2)
14: y= cos (arcsin ½ + arcsin 2/3)
(sqrt15 – 2)/6
(sqrt1/2)/15
2/3
-sqrt6
15: For questions 15 – 19: Solve each of the following equations for 0° ≤ θ < 360°.
2 cos θ = 1
280°
60°; 360°
40°
60°; 300°
16: (tan θ + 1) (sec θ – 1/2) = 0
120°; 300°
135°; 315°
65°; 300°
215°
17: sin2 θ + 3 sin θ + 2 = 0
270°
275°; 215°
119°
207°
18: sin θ/cos θ = tan2 θ
0°; 45°; 90°; 180°; 225°
180°; 225°
0°; 45°; 180°; 225°
45°; 225°
19: 4 sin θ cos θ = 1
90°; 145°; 225°
15°; 75°; 195°; 225°
25°; 145°
90°; 275°; 95°; 325°
20: For questions 20-23: Solve each of the following for x.
3y = 2 cos x + 1
x = arccos ((3y – 1)/2)
x = cos (3y/2)
x = 12
x = arccos ((2x +1)/3)
21: 2y = tan (x+3)
x = 2 arctan (y-3)
x = (arctan 2y) - 3
x = tan2 3
x = arctan (2/3)
22: Arctan x = arccot 1
x = 1
x = cot (2/3)
x = -1
x = 12
23: Arcsin x – arccos 1 = π/3
x = (sqrt3)/2
x = 3/2
x = - π/3
x = 1
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