Name ________________________
Pre-Calculus Honors
Problem Set #5.2
1. Solve for 0 ≤ 𝜃 < 2𝜋.
!
!
a) 𝑐𝑜𝑠(𝜃) = − "
b) 𝑠𝑖𝑛(𝜃) = − "
c) 𝑐𝑜𝑠(𝜃) = −1
1a) _______________________
1b) _______________________
1c) _______________________
!
d) 𝑐𝑜𝑠(2𝜃) = − "
!
e) 𝑠𝑖𝑛(2𝜃) = − "
f) 𝑐𝑜𝑠(3𝜃) = −1
1d) _______________________
1e) _______________________
1f) _______________________
2. Solve for all solutions of the equation (in radians).
a) 𝑐𝑜𝑠(𝜃) = −
√$
"
b) 𝑠𝑖𝑛(𝜃) =
√$
"
c) 𝑠𝑖𝑛(𝜃) = −1
2a) _______________________
2b) _______________________
2c) _______________________
d) 𝑐𝑜𝑠(2𝜃) = −
√$
"
e) 𝑠𝑖𝑛(3𝜃) =
√$
"
%
f) 𝑠𝑖𝑛 2$3 = −1
2d) _______________________
2e) _______________________
2f) _______________________
3. Solve for 0 ≤ 𝜃 < 2𝜋.
a) 𝑡𝑎𝑛(𝜃) = 1
b) 𝑡𝑎𝑛(2𝜃) = 0
c) 𝑐𝑜𝑡(𝜃) = −√3
3a) _______________________
3b) _______________________
3c) _______________________
d) 𝑠𝑒𝑐(2𝜃) = 1
e) 𝑐𝑠𝑐(𝜃) = 2
f) 𝑡𝑎𝑛(𝜃) = −√3
3d) _______________________
3e) _______________________
3f) _______________________
4. Solve for 0 ≤ 𝜃 < 360 (use calculator in degree mode, round to nearest degree)
a) 𝑐𝑜𝑠(𝜃) = −0.2
b) 𝑠𝑖𝑛(𝜃) = 0.3
c) 𝑡𝑎𝑛(𝜃) = 1.5
4a) _______________________
4b) _______________________
4c) _______________________
4 continued… Solve for 0 ≤ 𝜃 < 2𝜋 (use calculator and switch to radian mode, round to nearest tenth)
a) 𝑐𝑜𝑠(𝜃) = 0.88
b) 𝑠𝑖𝑛(𝜃) =
"
&
c) 𝑡𝑎𝑛(𝜃) = 11
4d) _______________________
4e) _______________________
4f) _______________________
5. Solve for 0 ≤ 𝜃 < 2𝜋.
a) sin" (𝜃) = 1
b) 4 cos" (𝜃) − 1 = 0
5a) _______________________
5b) _______________________
c) (tan 𝜃 − 1)(tan 𝜃 + 1) = 0
d) (cos 𝜃 + 1) (2cos 𝜃 − 1) = 0
5c) _______________________
5d) _______________________
6. Solve for 0 ≤ 𝜃 < 2𝜋.
a) 2 cos ! 𝜃 = cos 𝜃 + 3
b) 2𝑐𝑜𝑠 ! (𝜃) + √3𝑐𝑜𝑠𝜃 = 0
6a) _______________________
6b) _______________________
c) 3𝑠𝑒𝑐 ! (𝜃) − 2 = 0
d) (cos 𝜃 + 1) (2cos 𝜃 − 1) = −1
6c) _______________________
6d) _______________________
7. Solve for all solutions of the equation. Use a calculator and round radians to the nearest tenth where necessary.
a) tan! 𝜃 − 5tan 𝜃 + 6 = 0
7a) ___________________
b) 𝑐𝑜𝑠 ! (𝜃) + 3𝑐𝑜𝑠(𝜃) = 1
7b) __________________
c) 3 − 3𝑐𝑜𝑠(𝜃) = sin! (𝜃)
7c) __________________
d) −𝑠𝑒𝑐(𝜃) + 𝑡𝑎𝑛! (𝜃) − 1 = 0
7d) __________________
e) sin! (𝜃) − cos ! (𝜃) = 1 + 𝑐𝑜𝑠(𝜃)
7e) __________________
8. Solve for 0 ≤ 𝜃 < 2𝜋. Check your solutions by graphing both sides of the equation.
a) sin(𝜃) = cos(𝜃) + 1
8a) __________________
b) cot 𝜃 = cos 𝜃
8b) __________________
c) sin 𝜃 + √3cos 𝜃 = 1
8c) __________________
(use desmos for graph)