Question

Solve 8sin(4x)=4 for the two smallest positive solutions A and B, with A A= _________--

B = ________

Answer 1

• A = π/24
• B = 5π/24

Explanation:

You want two positive solutions to 8sin(4x) = 4.

Solution

Dividing by 8 gives ...

sin(4x) = 1/2

4x = arcsin(1/2) = π/6, 5π/6

Dividing by 4, we have ...

x = π/24, 5π/24

The two smallest positive solutions are ...

A = π/24

B = 5π/24

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Additional comment

When using a graphing calculator to solve an equation of this sort, we like to cast it as f(x) = 0. Then the solutions are the x-intercepts. In general, the equation can be written that way by subtracting the right-side expression from both sides. This gives us ...

8sin(4x) -4 = 0

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