How do I rearrange this equation involving trig functions to solve for x?

[Aristodol]

i am unsure about how to rearrange this equation so that I can solve for x an unknown angle. Please help.

we have:

sin^2 x(tan x)=1356

it is very simple I no but I just can't remember the way to go about solving this problem, especially because of the sin^2

 

[chanvincent]

Follow the steps below:

1. $$tan(x) = \frac{sin(x)}{cos(x)}$$
2. $$cos(x) = \sqrt{1 - sin^2(x)}$$
3. take square on both size, and re-arrange the terms, you will get a 6th order polynomial
4. do a substitution $$y = sin^2(x)$$, then you will have a 3th order polynomial
5. solve the 3rd order polynomial for y...
6. as soon as you have y, you will get x... (make sure x is not a single value function of y)

 

[Architeuthis Dux]

x term

To rearrange this equation, you can start by isolating the trig function with the unknown angle, which in this case is tan x. You can do this by dividing both sides of the equation by sin^2 x, which will give you:

tan x = 1356 / sin^2 x

Next, you can use the inverse trig function, arctan, to isolate the unknown angle x. This will give you:

x = arctan(1356 / sin^2 x)

However, since you are unsure about how to handle the sin^2 x term, it is important to note that you can also use the trig identity sin^2 x + cos^2 x = 1 to rewrite the equation as:

(sin x / cos x)^2 (tan x) = 1356

Then, you can substitute in the identity for sin^2 x and solve for tan x:

(tan x / cos^2 x) (tan x) = 1356

tan^2 x = 1356 / cos^2 x

Finally, you can take the square root of both sides to solve for tan x:

tan x = ±√(1356 / cos^2 x)

Remember that there are two possible solutions for x, so you will need to plug in both positive and negative values for the square root to find both solutions.

I hope this helps and remember to always check your solutions by plugging them back into the original equation to make sure they are correct.