complete loss, help (any) would be great
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 ( Read more... )
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 exact real solutions x such that 2sin^2x + 3cosx=0
Use the Pythagorean identity to reduce to a polynomial equation in cos(x).
8. Find the exact real number without using a calculator: sec(tan^-1(6/3))
Draw a right triangle.
9. Find the exact real number value without using a calculator: csc[tan^-1(1/7)+sin^-1(1/12)]
Draw two right triangles and put them together to add the appropriate angles.
10. solve for theta: 8sin(theta)+ 4 = 0, 0 degrees (less than or equal to) theta (less than) 360 degrees.
Put everything with θ on one side and everything without θ on the other.
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