# TrigonometrySolving a Trigonometric Equation

#### HelpMePlease

##### 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

##### Administrator
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

##### Administrator
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.

Sorry I can't help you yet but hopefully someone can soon.

#### 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

##### Administrator
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

##### Administrator
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

##### Administrator
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

##### Administrator
Staff member
re: Solving a Trignometric Equation

Yes, so far that makes sense.
Ok, great

After hitting "2nd", "Calc" click 2 or "zero". Now you'll be returned to the graph. This is a bit tricky to describe but I'll do my best.

If starts by asking for a left bound. Using the left/right buttons move the cursor to the LEFT side of the zero and click ENTER. Now it will ask for the right bound. Move the cursor to the RIGHT of the zero and click ENTER. Finally it will ask you to approximate the zero so just try to get it close to the zero and click ENTER.

If you did it right then the answer will show on your screen. What'd you get?