Help me out this engineering math ques....??!!!?

Question

For the equation

sin(5 x) = 0.14

find the smallest solution, the largest solution and the number of solutions for x in the interval 0 ≤ x ≤ 2π.

How to solve this?help me by giving the right answer..thx....

Answer 1

Look at the unit circle. Sin is the y axis, so sin=.14 for angle of about 8.05° and 180 - 8.05° = 171.95°. For engineering purposes, you need to use radians.

1. Smallest is when 5x = 8.05°, so just divide 8/5 (in radians) for smallest angle.

2. Since total angle is 5x, it will go to 10π, or 5 revolutions of the unit circle. Largest angle is 172° on last time around, or 360° * 4 + 172°. (convert to radians, of course).

3. Number of solutions is two per revolution, or 10.

Answer 2

I don't think the unit circle is the best way to look at this.

First forget the 0.14, just think sin (5x) or perhaps sin @.

Try this.  Let @ = 5x, therefor 0 <= @ <= 10π = 5 revolutions or cycles.

Now simply make the simple plot or graph for sin @ to 10π.  It will have five peaks.

Now draw a horizontal line at about 0.14, and ta da you have 10 times when sin (5x) = 0.14.  From the graph, you can figure the maximum and minimum, no?