1. Reference Angles?

Find the measurement of the reference angle of an angle measuring 5 pi divided by 4.
Answears
a. pi/2
b.-pi/2
c.pi/4
d. - pi/4

step by step explanation is 100% wanted and I will give thanks!
& just so I don't make another board. ..
Write cos 6x cos x - sin 6x sin x in terms of a single.. trigonometric function.. i only got to cos 7x - sin 7x
and write 2 cos(squared) 2 theta - 1 in terms of a single trigonometric function.
Use the half angle identity to evaluate tan 67.5degrees.
if i do tan(67.5dividedby 2) = sin67.5divided by 1+ cos67.5 how do i get
a.2squareroot(2)-2
b.squareroot(2) +1
c.squareroot(2) - 1
d. 2 - squareroot(2)
Find the exact value of cos 2 theta given that sin theta = - 3 divided by 5 and theta is in quadrant III,.
and last one i promiss after i get help with these i will try to help others to warm me up for my finals!
a. - 7/25
b. 7/25
c. 17/25
d. -17/25
please don't just give the answear but explain things! THAnKS!!

2. Trigonometry

Hello j0nath0n3
Originally Posted by j0nath0n3
Find the measurement of the reference angle of an angle measuring 5 pi divided by 4.
Reference angle: look here Reference Angle: How to find the reference angle as a positive acute angle
Originally Posted by j0nath0n3
Write cos 6x cos x - sin 6x sin x in terms of a single.. trigonometric function
Use $\cos A \cos B - \sin A \sin B = \cos (A+B)$ and the answer is simply $\cos 7x$
Originally Posted by j0nath0n3
write 2 cos(squared) 2 theta - 1 in terms of a single trigonometric function.
$\cos 2A = 2\cos^2 A -1$

So $\cos 4A = 2\cos^2 2A - 1$

Replace $A$ by $\theta$ in this second identity.

Originally Posted by j0nath0n3
Use the half angle identity to evaluate tan 67.5degrees.
$67.5 \times 2 = 135$ and $135 = 180 - 45$

So work from $\tan 135 = -\tan 45 =-1$, using $\tan \theta = \frac{2t}{1-t^2}$ and solve for $t$.

Originally Posted by j0nath0n3
Find the exact value of cos 2 theta given that sin theta = - 3 divided by 5 and theta is in quadrant III
Use $\cos 2\theta = 1-2\sin^2\theta$ and just plug the number $-\frac{3}{5}$ in.

3. where do i plug -3/5 in? and i dont get how you do multiply 67.5 ?? Thanks for all the others though!

4. Trigonometry

Hello j0nath0n3
Originally Posted by j0nath0n3
Use the half angle identity to evaluate tan 67.5degrees.
and

So work from , using and solve for .
Let $\tan 67.5^o = t$.

Then $\tan 135^o = \tan (2 \times 67.5^o) = \frac{2t}{1-t^2} = -1$.

$\Rightarrow 2t = -1(1-t^2) = t^2 - 1$

$\Rightarrow t^2 -2t - 1 = 0$

Factorise and solve for $t$, bearing in mind that $\tan 67.5^o > 0$

Originally Posted by j0nath0n3
Find the exact value of cos 2 theta given that sin theta = - 3 divided by 5 and theta is in quadrant III
Use and just plug the number in.
$\sin\theta = -\frac{3}{5}$

$\Rightarrow \cos 2\theta = 1 - 2\sin^2\theta$

$= 1 - 2 \times \left(-\frac{3}{5}\right)^2$

$= 1 - 2\times \frac{9}{25}$

$= \frac{7}{25}$