Solving Closest Values of x to Zero: Formula to Make it Easy

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To solve the equation -30 sin(3x) = 1/10 cos(3x) for values of x closest to zero, one can transform the equation into a tangent form by dividing both sides by cos(3x), leading to -30 tan(3x) = 1/10. This formulation simplifies the problem by allowing the use of trigonometric identities. A right triangle can be used to visualize the relationship between sine, cosine, and tangent, reinforcing the understanding of the equation. Utilizing this approach can help find the two values of x that satisfy the condition. This method effectively streamlines the process of solving for x.
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I am having trouble solving for the two values
of (x) that are closest to zero.

-30 sin 3x = 1/10 cos 3x

Is there a formula I could use to make this easy?
 
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Write this as an equation in tan(3x)..
 
sin(x)/cos(x) = tan(x)

to see why this is true Draw a right triangle with hypotenuse 1 and an acute angle x, you can work the sides of the right triangle have lengths sin(x) and cos(x).
 
Oh yea! I just forgot!

Thank you!
 

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