[Math] what does tangent mean

circlestrigonometry

I need your help, my question is what does tangent value mean and how can we benefit from it ?

I know that $\tan(\theta) = \dfrac{\sin(\theta)}{\cos(\theta)}$, but what does that mean?

Sorry I am not good in mathematics so I need your help.

Best Answer

Well, tangent has a few "meanings", of which $\frac{\sin{\theta}}{\cos{\theta}}$ is but one.

Another important one is the fact that tangent describes slope. If I were to construct an angle with the initial ray on the positive X-axis, and the terminal ray in some direction, the "slope" of the terminal ray is the tangent of the angle. You can also see this in the right triangle that is used for basic trig definitions, where tangent is $\frac{\text{opposite}}{\text{adjacent}}$, which is, in a way, the "slope" of the hypotenuse.

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