MHB Tan (Theta - Pie) Answer Explained

[captainnumber36]

What does Tan (Theta - Pie) = ?

I know Tan (theta + pie) = tan (theta).

They say the answer is tan (theta), but I think it's some kind of typo.

 

[MarkFL]

What does Tan (Theta - Pie) = ?

I know Tan (theta + pie) = tan (theta).

They say the answer is tan (theta), but I think it's some kind of typo.

Pie is a dessert, while pi is a Greek letter used to represent the ratio of a circle's circumference to its diameter. Having said that, the period of the tangent function is $\pi$ radians, which means:

$$\tan(\theta+\pi k)=\tan(\theta)$$ where $k\in\mathbb{Z}$ (this means $k$ can be any integer, even negative ones)

So, it's not a typo, your book is correct.

 

[skeeter]

What does Tan (Theta - Pie) = ?

I know Tan (theta + pie) = tan (theta).

They say the answer is tan (theta), but I think it's some kind of typo.

sum/difference identity for tangent ...

$\tan(a \pm b) = \dfrac{\tan{a} \pm \tan{b}}{1 \mp \tan{a} \cdot \tan{b}}$

now, let $a = \theta$ and $b = \pi$ ... substitute & evaluate