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

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- Jan 28th 2009, 05:23 PMSoYahSolving the Sine Equation
solve the equation sin x=0.2 on the interval 0 is less than or equal to x is than (2pi)

- Jan 28th 2009, 05:33 PMMush
$\displaystyle \sin(x) = \frac{1}{5} $

On way to solve this is to write:

$\displaystyle 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 $\displaystyle 2\sqrt{6} $

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