HalfandDoubleAngleIdentitiesPracticeProblems
1. Whatistheexactvalueof2 sin(15˚) cos(15˚)?
E
KL
F
F
2. Iftan 𝜃 = ,where𝜋 < 𝜃 <
,findtheexactvalueof:
a. sin 2𝜃 b. cos 2𝜃 c. tan 2𝜃 3. Iftan 𝜃 = −3andsin 𝜃 < 0,findtheexactvalueof
a. cos 2𝜃 b. sec 2𝜃 4. Ifcos 𝜃 =
R S
K
L
,where < 𝜃 < 𝜋,findtheexactvalueof:
F
a. tan(2𝜃)
b. cos(2𝜃)
K
L
T
F
5. Ifcos 𝜃 = ,where0 < 𝜃 < ,findtheexactvalueof:
a. sin 2𝜃 b. cos
U
c. tan
U
F
F
6. Usingtheinformationfoundin#3,findtheexactvalueof:
7.
a. sin
U
b. cos
U
c. tan
U
F
F
F
ThefollowingvaluescanbefoundusingSum,Difference,Half-Angle,andDouble-Angle
Identities.Forthosethatcanbefoundusingdifferentidentities,solveatusingtwo
identitiestocheckyoursolution.Forallproblemsyouareencouragedtocheckyour
solutionusingagraphingcalculator.
8. tan(15˚)
9. cos −22.5˚ 10. csc
cL
d
11. cos F (15˚) + sinF (15˚)
12. sin(−285˚)
13. sec(165˚)
14. cos F (75˚) − sinF (75˚)