Trig Help Please. Radians?

Crosses x axis when y = 0

sin [ 2x - π/2 ] = 0

2x - π/2 = 0 , π , 2π , 3π , 4π -----------------

2x = π/2 , 3π/2 , 5π/2 , 7π/2 , 9π/2 -----------------

x = π/4 , 3π/4 , 5π/4 , 7π/4 , 9π/4--------------------

x = π/4 + ( 2 k+1 ) π/4 for k = 0 , 1 , 2 , 3 , 4 -------------

well, crossing the x-axis means y=0. So, you have:

1/2 sin (2x - pi/2) = 0

sin (2x-pi/2)=0

you know sin(X)=0 at X=0 modulo pi, meaning X=0, pi, 2 pi, 3 pi, etc...

So 2x-pi/2=0 (mod pi)

2x=pi/2 (mod pi)

x=pi/4 (mod pi/2)

So, here you have it x =pi/4, pi/4+pi/2 (=3pi/4), etc...

You can actually see that from the graph. You can just graph the function, and you will see the curve cross at x=pi/4, etc.

Radians are units of angle on a circle. You could use degres instead of radians, but in math people use radians. Radians are usually expressed in terms of pi. You draw a circle of radius 1. You go around the circle counter-clockwise. You start at 0 degres/radians. Once you are at the top of the circle, that's pi/2 radians (90 degres). Once you are at the very left, that's pi (180 degres), At the bottom, that's 3pi/2 (270 degres); then you are back to the right, at the origin (0 radians or 2pi radians; or 0 degres or 360 degres). Because you can go around the circle more than once, and because you are measuring angles, 0 degres is the same as 360 degres. In radians, 0 is the same as 2 pi.

A sine or a cosine function is simply the sine or cosine of a point on that circle. If x=0 (origin) then cos(0)=1 and sin(0)=0; at the top, cos(pi/2)=0 and sin(pi/2)=1. So, y=sin(x) means that you will move around the circle counter-clockwise. x will be the angle in radians, and y will be the sine of that angle. As x goes around the circle again and again, the sine goes from 0 to 1 to 0 to -1 back to 0 and it repeats.

When it crosses on the x axis the y=0

0 =(1/2)sin(2x-(pi/2))

sin(2x-(pi/2)) =0

2x-pi/2 = n * pi [n = 0 +/- 1 +/- 2]

2x = n *pi + pi/2 = 1/2 * pi (2n +1)

x = 1/4 * pi (2n +1)

So, it crosses on the x axis at pi/4, 3pi/4, -pi/4, and other odd (positive or negative) multiples of pi/4

x-intercepts ---->y = 0

solve sin(2x- (pi/2)) = 0 ----->2x - pi/2 = k pi , with k = 0, 1, -1, 2, -2, ...

then you can find x values

set y=0 then solve for x to find the point it crosses on the x-axis.

for radian points, you can refer to this wikipedia article.

http://www.google.com.sg/search?hl=en&rlz=1T4PCTA_...