Given that 4 sin(x) + 5 cos(x) = 0 , find the value of tan x .

Before we get started with answering the question, it is generally good practice to write down any formulas and equations you know that will help us work through the solution. So what formula do we know that links sin(x), cos(x), and tan(x) ?

That's right: sin(x)/cos(x) = tan(x). (Well done!)

Since the question is asking you to find the value of tan(x), this means that we need to find a way to "manipulate" this equation so that tan(x) shows up. Luckily, we have the right tools required to do this (above). So now it is simply a matter of rearranging this equation.

Step 1:  4 sin(x) + 5 cos(x) = 0
Step 2: Rearrange this so that you get 4 sin(x) = - 5 cos(x)
Step 3: Think back to the formula. Divide both sides by cos(x) to get 4 tan(x) = -5
Step 4: We have the value of 4 tan(x), but we want tan(x). So what do we do? Correct again - divide both sides by 4 to get tan(x) = -5/4, or tan(x) = -1.25, in decimals. 

Hooray! But we're not done here. Another good practice is to take the answer and substitute it back into the original equation, to check that both sides of the equation are equal with this value of tan(x). If it is...

We're done :)