# Math Help - Reference Angles?

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.
$\sin\theta = -\frac{3}{5}$

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

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

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

$= \frac{7}{25}$