i have a study guide for a quiz tomorrow, but i am not sure how to solve a few of the problems and feel pretty unprepared. it would be great if anyone could help me with these:
use the interval (0, 2 pi)
1. 2sin^2(theta)-sin(theta) = 1
2.(3cot^3)x-cotx= Square root of 3
3. (2sin^2)2theta = 1
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1. (2cos^2)2x-cos2x-1 in radians
2. (12sin^2)x-5sinx-2 for the interval (0,360) in degrees
(im not sure exactly what the last two are asking for you to do, so hopefully someone recognizes it)
thank you
Jimmie,
I have the first one for you:
2sin^2(theta) - sin(theta) - 1 = 0
(2sin(theta) + 1) (sin(theta) -1) = 0
using the zero factor rule, sin(theta) = 1 and -1/2
On the unit circle these sin values match with /2, 7 /6, and 11 /6,
But because the angle was referred by the term "theta" I should give the answer in degrees. So the answers would be 90 degrees, 210 degrees and 330 degrees.
~sif