SOLUTION: what is the solution set of all angles in [0,2pi) 4 cos^2x-3=0 5 sec^2x-20=0 2 cos^2 x-sin x-1=0

Question 756390: what is the solution set of all angles in [0,2pi)
4 cos^2x-3=0

5 sec^2x-20=0

2 cos^2 x-sin x-1=0
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
what is the solution set of all angles in [0,2pi)
4 cos^2x-3=0
cos^2(x) = 3/4
cos(x) = sqrt(3)/2
x = pi/3 or x = (5/6)pi
============================
5 sec^2x-20=0
sec^2(x) = 4
sec(x) = +2 or -2
x = pi/6 or (11/6)pi or (5/6)pi or (7/6)pi
===================================================
2 cos^2 x-sin x-1=0
2(1-sin^2(x)) - sin(x) - 1 = 0
-2sin^2(x) - sin(x) + 1 = 0
----
2sin^2(x) + sin(x) - 1 = 0
-----
(2sin(x)-1)(sin(x)+1) = 0
sin(x) = 1/2 or sin(x) = -1
x = pi/6 or (5/6)pi or (3/2)pi
==================================
Cheers,
Stan H.
===================

RELATED QUESTIONS
Find all solutions of each of the equations in the interval (0, 2pi) cos(x- pi/2) +... (answered by lwsshak3)

Solve the equation for x, on the interval 0 is less than or equal to x and 2pi is greater (answered by Alan3354)

I'm attempting to do corrections on a test, but these three questions are giving me... (answered by stanbon,Edwin McCravy)

Find all the solutions between 0 and 2pi to the equation... (answered by ewatrrr)

Find the solution of the equation for [0,2pi] 2(tan(theta))-(sec^2(theta))=0 Here... (answered by Alan3354)

2sec^2 x-5 sec x+2=0 cos 2x-2 sinx- cos^2... (answered by greenestamps)

Find all values of x in the interval (0, 2pi) that satisfy the condition: ((csc^2)x)-1=4 (answered by lwsshak3)

Solve on the interval [0, 2pi] Sin*2x - sin x + 1=... (answered by lwsshak3)