# 100sin(alpha) = 500cos(alpha) - how do you solve such a thing?

• Femme_physics
In summary, the conversation is about solving the trigonometric equation 100sin(alpha) = 500cos(alpha), with the person asking for help on how to approach the equation since there are two functions involved. The expert suggests squaring both sides or dividing by cosine to simplify the equation.

#### Femme_physics

Gold Member
100sin(alpha) = 500cos(alpha) ---- how do you solve such a thing?

100sin(alpha) = 500cos(alpha)

I see there's only one unknown, but I'm a little befuddled how to approach trigo equations like that when the angle is unkown (I know about the arc-cos/sin/tan function) but there are 2 functions in the equation! Cosine AND Sine! Arg... perhaps you guys can help me with a short guide/link/whatever...

I'll appreciate the help :)

-Dory

Why don't you square both sides. Do you know of any relation relating squares of sines and cosines?

Or even more simply, divide through by $$\cos(\alpha)$$

Thanks! Right, I forgot that sine/cosine is tan! :) That simplifies things!

Mentallic said:
Or even more simply, divide through by $$\cos(\alpha)$$

Oh! :P

## What does the equation "100sin(alpha) = 500cos(alpha)" represent?

This equation represents a mathematical relationship between the sine and cosine of an angle alpha. It shows that the product of 100 and the sine of alpha is equal to the product of 500 and the cosine of alpha.

## What does it mean to "solve" this equation?

Solving this equation means finding the value of alpha that satisfies the equation. In other words, we are looking for the angle or angles that make the equation true.

## How do you solve this equation?

To solve this equation, we can use trigonometric identities and properties to manipulate the equation and isolate the variable alpha. One method is to divide both sides by cos(alpha) to get tan(alpha) = 100/500, and then use inverse tangent to find the value of alpha.

## Are there other methods for solving this equation?

Yes, there are other methods such as using the Pythagorean identity (sin^2(alpha) + cos^2(alpha) = 1) or using a trigonometric table or calculator to find the values of the sine and cosine of alpha and then solving for alpha.

## What are the possible solutions to this equation?

Since the sine and cosine of an angle can have multiple values, there can be multiple solutions to this equation. In this case, alpha can have infinite solutions because the sine and cosine of an angle can repeat every 360 degrees. However, we can restrict the solutions to a specific range, such as 0 to 360 degrees, to get a finite set of solutions.