# TrigonometrySolving a Trigonometric Equation

##### New member
2Cos (3/10x) - 3Sin(1/2x)=0

How would I go about solving this equation? I do not even know where to begin.

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#### Jameson

Staff member
re: Solving a Trignometric Equation

Hi there,

Welcome to MHB! Can you confirm that this is your problem $$\displaystyle 2\cos \left( \frac{3}{10}x \right) -3\sin \left( \frac{1}{2}x \right)=0$$?

Jameson

#### InNeedOfHelp

##### New member
re: Solving a Trignometric Equation

Thanks.
Yes, that's the equation.

#### Jameson

Staff member
re: Solving a Trignometric Equation

Thanks.
Yes, that's the equation.
Please use just one account. There's no reason to have two.

Ok, so this is a tricky problem. I don't see any way of solving explicitly yet using standard trig formulas. Here's what Wolfram says. What course is this for? What is the topic you are currently studying? That might help us see what your professor wants.

#### InNeedOfHelp

##### New member
re: Solving a Trignometric Equation

Trigonometry
We have went over simplifying identities, finding exact solutions of identities, things of that sort.

I accidentally left out the interval if that helps any?

The answer is in decimal form.

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#### MarkFL

Staff member
re: Solving a Trignometric Equation

If the answer is given in decimal form, then you are probably expected to use the root-finding function of your calculator. There is only one root on the given interval. If this were for a calculus course, then you could use Newton's method to approximate the root, but since it is for a course in trigonometry, I suspect you are to use a calculator.

What type of calculator do you have?

#### InNeedOfHelp

##### New member
re: Solving a Trignometric Equation

A TI-83 Plus

#### MarkFL

Staff member
re: Solving a Trignometric Equation

I have a TI-89 Titanium, and when I enter:

solve(2cos(3x/10)-3sin(x/2)=0,x)

I find one solution given on the given interval. Does yours have a solve function?

#### Jameson

Staff member
re: Solving a Trignometric Equation

All of this info is good to state in the first post so we know the context of your problem.

1) Graph $$\displaystyle 2\cos(.3x)-3\sin(.5x)$$
2) Click "Zoom", and choose "ZStandard" (or just hit 6)
3) You'll see just one zero in the domain [0,6]. It's around 1. To calculate the zero, click "2nd" then "Calc" (Calc is in yellow, the main button is "Trace")

Does this make sense so far?

#### InNeedOfHelp

##### New member
re: Solving a Trignometric Equation

Yes, so far that makes sense.

#### Jameson

Ok, great 