You can
put this solution on YOUR website!
Solve each equation on the interval 0
That's way too many problems to post! I'll solve only 3,6, and 12.
and give only the answers to the rest. BTW, 0 is a number, not an
interval. So I can't tell if you want them in
degrees or radians. I gave them in radians. If you want degrees,
multiply by 180/pi.
1. cos^2(x)-sin^2(x)+sin(x)=0 pi/2, 7pi/6, 11pi/6
2. sin^2(x)= 6(cosx+1), pi
3. 2sin^2(x)= 3(1-cosx), 0, pi/3, 5pi/3
2(1 - cos²x) = 3(1 - cosx)
2(1 - cosx)(1 + cosx) = 3(1 - cosx)
2(1 - cosx)(1 + cosx) - 3(1 - cosx) = 0
(1 - cosx)[2(1 + cosx) - 3] = 0
(1 - cosx)[2 + 2cosx - 3] = 0
(1 - cosx)(2cosx - 1) = 0
setting first factor = 0
1 - cosx = 0
-cosx = -1
cosx = 1
x = 0
setting second factor = 0
2cosx - 1 = 0
2cosx = 1
cosx = 1/2
x = pi/3, 5pi/3
4. cos(x)=sin(x), pi/4, 5pi/4
5. cos(x)+sin(x)=0 3pi/4, 7pi/4
6. tan(x)=2sin(x), 0, pi/3, pi, 5pi/3
sinx/cosx = 2sinx
sinx = 2sinx·cosx
sinx - 2sinx·cosx = 0
sinx(1 - 2cosx) = 0
setting first factor = 0
sinx = 0
x = 0, pi
setting second factor = 0
1 - 2cosx = 0
-2cosx = -1
cosx = 1/2
x = pi/3, 5pi/3
7. 1+sin(x)=2cos^2(x), pi/6, 5pi/6, 3pi/2
8. sin^2(x)=2cos(x)+2, pi
9. tan^2(x)= 3/2 sec(x), pi/3, 5pi/3
10. csc^2(x)=cot(x)+1, pi/4, pi/2, 5pi/4, 3pi/2
11. sec^2(x)+tan(x)=0, no solution
12. sec(x)=tan(x)+cot(x), no solution
1/cosx = sinx/cosx + cosx/sinx
Multiply thru by LCD = cosx·sinx
sinx = sin²x + cos²x
sinx = 1
x = pi/2
However we must discard that solution
because the original problem contains
tanx, and tan(pi/2) is not defined.
13. sin(x)- [square root of 3]cos(x)= 1, pi/2, 7pi/6
Edwin
