On a monitor, the graphs of two impulses are recorded on the same screen, where 0°≤ x < 360°. The impulses are given by the following equations:
y = 2 sin2 x
y= 1 - sin x
Find all values of x, in degrees, for which the two impulses meet in the interval 0°≤ x < 360°.
2007-04-10 03:59:06 · 2 answers · asked by Celia 4 in Science & Mathematics ➔ Mathematics
I spent 20 minutes trying to solve it thinking the 1st equation said y = 2sin(2x). That's only solvable graphically. But if the 1st equation is y = sin² x, then
2sin² x = 1 - sin x
2sin² x + sin x - 1 = 0
(2sin x - 1)(sin x + 1) = 0
2sin x - 1 = 0
sin x = 1/2
x = 30° or x = 150°
sin x + 1 = 0
sin x = -1
x = 270°
2007-04-10 04:31:01 · answer #1 · answered by Philo 7 · 0⤊ 0⤋
When in doubt, draw a picture!
The easiest and most visual way to find out when these two graphs intersect is to draw both of these graphs.
From a more "mathy" way to do this, you set one equation equal to the other, and solve for the different values of x over the range of 0 to 360 degrees
ie:
2*sin2x = 1 - sinx
2007-04-10 11:03:56 · answer #2 · answered by Joe the Engineer 3 · 0⤊ 0⤋