Question

solve cos(2beta-pi/2)=-1
where 0 12 years ago

Answer 1

For what angle is cosine -1?

Answer 2

cos(pi)=-1

Answer 3

correct. Equate 2beta - pi/2 and pi and solve for beta.

Answer 4

cos(2beat-pi/2)=pi + 2pi k, where k is an integer

Answer 5

how do I get cos beta by it self?

Answer 6

Yes. Solve for beta

Answer 7

cos(2beta-pi/2) = cos(pi + 2pi k), where k is an integer.
Therefore, (2beta-pi/2) = (pi + 2pi k)
Solve for beta.

Answer 8

oh i got it thanks!!!

Answer 9

If cos(A) = cos(B)
then A = B + 2kpi where k is any integer (positive, zero or negative).

Here, cos(2beta - pi/2) = cos(pi)
Therefore, 2beta - pi/2 = pi + 2kpi.
Add pi/2 to both sides:
2beta = pi + 2kpi + pi/2 = 3/2pi + 2kpi
divide both sides by 2:
beta = 3/4pi + kpi
Here we want beta to be in the range [0, 2pi]. Negative integer values for k will yield negative angle for beta and therefore can be ignored. Try k = 0, 1, 2 and stop when it goes past 2pi.

You are welcome.