find all solutions in the interval [0,360degrees) sin(5x)=0
To find all solutions in the interval [0, 360 degrees) for the equation sin(5x) = 0, you can follow these steps:
Step 1: Recall the unit circle and identify the angles where sin(θ) = 0. In the unit circle, these angles occur at 0 degrees, 180 degrees, 360 degrees, and so on. These angles are multiples of π radians.
Step 2: Set up the equation sin(5x) = 0 and solve for x. Divide both sides of the equation by sin(5x):
sin(5x) / sin(5x) = 0 / sin(5x)
This simplifies to:
1 = 0
Since this is not a true statement, it means there are no solutions for which sin(5x) equals 0.
Therefore, in the interval [0, 360 degrees), there are no solutions for the equation sin(5x) = 0.
sin 5 x = 0
well, zero and every time 5 x is a multiple of 180
if x = 0 , sin 5 x = 0
if x = 180/5 = 36, sin 5 x = 0
if x = 360/5 = 72
in fact for any multiple of 36 until we reach 9
9 * 36 = 324 and sure enough sin 5*324 = sin 1620 = 0