Question #8834

On the monitor, the graphs of two impulses are recorded on the same screen, where 0°≤x≤360°. The impulses are give by the following equations.
y=2sin²x
y=1-sinx
Find all values x, in degrees, for which the two impulses meet in the interval 0°≤x≤360°. [Only an algebraic solution will be accepted.]

Expert's answer

Let's consider an equation:

2sin²x = 1-sinx, 0°≤x≤360°.

2sin²x + sinx - 1 = 0 ==> sinx = (-1 ± 3)/4, so sinx = 1/2 or sinx = -1.

Taking into account that 0°≤x≤360°,

sinx = 1/2 ==> x = 30°;

sinx = -1& ==> x = 270°.

So, there are two points of intersection: 30° and 270°.

2sin²x = 1-sinx, 0°≤x≤360°.

2sin²x + sinx - 1 = 0 ==> sinx = (-1 ± 3)/4, so sinx = 1/2 or sinx = -1.

Taking into account that 0°≤x≤360°,

sinx = 1/2 ==> x = 30°;

sinx = -1& ==> x = 270°.

So, there are two points of intersection: 30° and 270°.

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