MCR3UI
1.
Solve each of the following equations to the nearest degree, 0 ≤ 𝜃 ≤ 360°.
a) sin 𝜃 = 0.1234
b) cos 𝜃 = 0.3472
c) tan 𝜃 = 1.5732
d) sin 𝜃 = −0.7512
e) cos 𝜃 = −0.7851
f) tan 𝜃 = −0.3125
2.
Solve each of the following equations. Write your answer to the nearest degree.
a) 5 sin 𝜃 + 3 = sin 𝜃 + 2, 0 ≤ 𝜃 ≤ 360°
b) 7 sin 𝜃 − 11 = 4 sin 𝜃 − 13, 0 ≤ 𝜃 ≤ 360°
c) 7 − 11 cos 𝜃 = 8 − 8 cos 𝜃, 0 ≤ 𝜃 ≤ 360°
d) 25 + 15 tan 𝜃 = 12 tan 𝜃 + 28, 0 ≤ 𝜃 ≤ 360°
3.
Solve each of the following equation, for 0 ≤ 𝑥 ≤ 360°. Answers must be exact.
a) √2 cos 𝑥 − 1 = 0
b) 2 sin 𝑥 − √3 = 0
c) 2 sin 𝑥 + 1 = 0
4.
Solve each of the following equations, for 0 ≤ 𝑥 ≤ 2𝜋. Answers must be exact.
a) 2 cos 𝑥 + 1 = 0
b) √2sin 𝑥 + 1 = 0
c) tan 𝑥 − 1 = 0
3a) 45°, or 315°
3b) 60° or 120°
3c) 210° or 330°
4a)
3
2𝜋
or
3
4𝜋
4b)
4
5𝜋
or
4
7𝜋
4c)
4
𝜋
or
4
5𝜋
Answers
1a) 𝜃 = 7° 𝑜𝑟 173° 1b) 𝜃 = 70° 𝑜𝑟 290° 1c) 𝜃 = 58° 𝑜𝑟 238° 1d) 𝜃 = 229° 𝑜𝑟 311° 1e) 𝜃 = 142° 𝑜𝑟 218°
2a) 𝜃 = 194° 𝑜𝑟 346° 2b) 𝜃 = 222° 𝑜𝑟 318° 2c) 𝜃 = 109° 𝑜𝑟 251° 2d) 𝜃 = 45° 𝑜𝑟 225°
1f) 𝜃 = 163° 𝑜𝑟 343°
MCR3UI
Date: _________________________
1.
Solve each of the following equations to the nearest degree, 0 ≤ 𝜃 ≤ 360°.
a) sin 𝜃 = 0.1234
b) cos 𝜃 = 0.3472
c) tan 𝜃 = 1.5732
d) sin 𝜃 = −0.7512
e) cos 𝜃 = −0.7851
f) tan 𝜃 = −0.3125
2.
Solve each of the following equations. Write your answer to the nearest degree.
a) 5 sin 𝜃 + 3 = sin 𝜃 + 2, 0 ≤ 𝜃 ≤ 360°
b) 7 sin 𝜃 − 11 = 4 sin 𝜃 − 13, 0 ≤ 𝜃 ≤ 360°
c) 7 − 11 cos 𝜃 = 8 − 8 cos 𝜃, 0 ≤ 𝜃 ≤ 360°
d) 25 + 15 tan 𝜃 = 12 tan 𝜃 + 28, 0 ≤ 𝜃 ≤ 360°
3.
Solve each of the following equation, for 0 ≤ 𝑥 ≤ 360°. Answers must be exact.
a) √2 cos 𝑥 − 1 = 0
b) 2 sin 𝑥 − √3 = 0
c) 2 sin 𝑥 + 1 = 0
4.
Solve each of the following equations, for 0 ≤ 𝑥 ≤ 2𝜋. Answers must be exact.
a) 2 cos 𝑥 + 1 = 0
b) √2sin 𝑥 + 1 = 0
c) tan 𝑥 − 1 = 0
**These questions are from the Mathematics 11 textbook, published by McGraw-Hill Ryerson in 2001**
3a) 45°, or 315°
3b) 60° or 120°
3c) 210° or 330°
4a)
3
2𝜋
or
3
4𝜋
4b)
4
5𝜋
or
4
7𝜋
4c)
4
𝜋
or
4
5𝜋
Answers
1a) 𝜃 = 7° 𝑜𝑟 173° 1b) 𝜃 = 70° 𝑜𝑟 290° 1c) 𝜃 = 58° 𝑜𝑟 238° 1d) 𝜃 = 229° 𝑜𝑟 311° 1e) 𝜃 = 142° 𝑜𝑟 218°
2a) 𝜃 = 194° 𝑜𝑟 346° 2b) 𝜃 = 222° 𝑜𝑟 318° 2c) 𝜃 = 109° 𝑜𝑟 251° 2d) 𝜃 = 45° 𝑜𝑟 225°
1f) 𝜃 = 163° 𝑜𝑟 343°