Question

Find cot θ if csc θ = sqr5/2 and tan θ > 0.
also
Verify the identity.
cos 4u = cos22u - sin^2 (2u)
Find the exact value by using a half-angle identity.
cos(pi/12)

Answer 1

csc positive means sin positive

sin and tan are positive in 1st Quadrant

Answer 2

\[\Large \cot \theta = \frac AO=\frac12\]

Answer 3

sorry i have the first one its the other two i need help with

Answer 4

4u = 2 * 2u
Use the double angle identity of cosine.

Answer 5

im still confused

Answer 6

\[
\cos(2a) = \cos^2(a) - \sin^2(a) \\
\cos(4u) = \cos(2*2u) = \cos^2(2u) - \sin^2(2u) \\
\]

Answer 7

the actual problem is cos4u=cos^2(2u)-sin^(2u)

Answer 8

The first line in the previous reply is a well-known trig identity.
The second line in the previous reply answers your problem.

Answer 9

oh ok i see

Answer 10

thank you

Answer 11

now i just need help with the second one

Answer 12

\[
\cos(2a) = 2\cos^2(a) - 1 \\
\text{Let }a = \frac{\pi}{12} \\
\cos(2* \frac{\pi}{12}) = 2\cos^2(\frac{\pi}{12}) - 1 \\
\cos(\frac{\pi}{6}) = 2\cos^2(\frac{\pi}{12}) - 1 \\
\frac{\sqrt{3}}{2} = 2\cos^2(\frac{\pi}{12}) - 1 \\
\frac{\sqrt{3}}{2} + 1 = 2\cos^2(\frac{\pi}{12}) \\
\frac{\sqrt{3}+2}{2} = 2\cos^2(\frac{\pi}{12}) \\
\frac{\sqrt{3}+2}{4} = \cos^2(\frac{\pi}{12}) \\
\cos^2(\frac{\pi}{12}) = \frac{\sqrt{3}+2}{4} \\
\cos(\frac{\pi}{12}) = \frac{\sqrt{\sqrt{3}+2}}{2} \\
\]

Answer 13

thank you dude

Answer 14

do you think you have a little more time because the review only has 3 more questions?

Answer 15

what is tan(x) if cos(x)=1/4 and sin(x) <0

write with only sin and cos: sin(3x)-cosx
and
verify the identity sin(x+pi/2)=cos(x)

Answer 16

Use the same method shown for the previous problem.
Draw a triangle. Use the definition of cosine to mark the proper sides with 1 and 4. Find the third side. Use definition of tan(x) to find its value. Since tan = sin/cos and sin < 0 and cos > 0, tan < 0.

Answer 17

alright

Answer 18

ok i got sqr 15