# Solving the Sine Equation

• January 28th 2009, 05:23 PM
SoYah
Solving the Sine Equation
solve the equation sin x=0.2 on the interval 0 is less than or equal to x is than (2pi)
• January 28th 2009, 05:33 PM
Mush
Quote:

Originally Posted by SoYah
solve the equation sin x=0.2 on the interval 0 is less than or equal to x is than (2pi)

$\sin(x) = \frac{1}{5}$

On way to solve this is to write:

$x = \arcsin(\frac{1}{5})$, and simplify plug it into your calculator.

Another way is to consider a triangle. If you take the sin of an angle in a triangle, it gives the ratio of the length of the side opposite that angle and the hypotenuse.

Hence the hypotenuse of our triangle is 5, and the opposite side from angle x is 1. From pythagorus we calculate that the side adjacent to the angle x is $2\sqrt{6}$

Now you know all lengths, you can work out the angle using the cosine rule.