complete loss, help (any) would be great

[chriscrone]

1.  Simplify the following expression using fundamental identities: (1-cos^2 theta)/sin theta.

2.  Verify the identity: (tan x - sec x)/ sin x = (1- csc x) sec x.

3.  In which quadrants is cos x = -(square root of 1- sin^2 x)  (true)

4.  Verify the identity: 2 sin x cos x = sin2x

5.  What is the exact value of : cos^4 (pi/8) + sin^4 (pi/8) - 2sin^2

Comments

[ressie_noldo]

1 -- 1 -cos^2 is sin^2. sin^2 by sin is sin theta. (assuming everything is positive and non-zero, but I suspect that would be okay.)

2. Take sin inside and divide each term by it. tan/sin is 1/cos (as tan is sin/cos); sec/sin is sec(cosec) (because 1/sin is cosec). Therefore it's (1/cos -sec(csc)), which (taking out sec) is (sec)(1-csc)

3. True whenever cos is negative, because square root is always the positive root. So second and third quadrants.

Will get back to the others in a bit.

[chriscrone]

thank you so much

[joshua_green]

1. Simplify the following expression using fundamental identities: (1-cos^2 theta)/sin theta.
You'll need the Pythagorean identity sin2(θ) + cos2(θ) = 1.

2. Verify the identity: (tan x - sec x)/ sin x = (1- csc x) sec x.
Convert everything to sin(x)'s and cos(x)'s.

3. In which quadrants is cos x = -(square root of 1- sin^2 x) (true)
We always have the Pythagorean identity.  If we solve for cos(x), we have a choice of which square root to choose.  Use the fact that cos and sin can be defined in terms of coordinates of points on the unit circle.

4. Verify the identity: 2 sin x cos x = sin2x
I'm not sure what is meant by "verify" here.

5. What is the exact value of : cos^4 (pi/8) + sin^4 (pi/8) - 2sin^2 (pi/8) cos^2 (pi/8)
This factors. One particular formula at http://mathworld.wolfram.com/TrigonometricAdditionFormulas.html will come in handy.

6. Find the exact real solutions over the indicated interval: sin x = tan x, 0 (less than or equal to) x (less than or equal to) 2pi.
Start with tan(x) = sin(x)/cos(x).

7. Find all

[joshua_green]

For 4, draw two right triangles, each with an angle of x, and put them together to add those angles.

[chriscrone]

thank you so much

[joshua_green]

BTW, an easier way to do 9 might be to use an appropriate Trigonometric Addition Formula (provided that you're allowed to use it without proof).