- #1

captainnumber36

- 9

- 0

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

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

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So, in summary, the identity for tangent of the sum/difference of two angles can be used to show that Tan (Theta - Pie) = tan (theta) is not a typo, but rather a valid mathematical statement.

- #1

captainnumber36

- 9

- 0

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

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

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- #2

MarkFL

Gold Member

MHB

- 13,288

- 12

captainnumber36 said:

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:

\(\displaystyle \tan(\theta+\pi k)=\tan(\theta)\) 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.

- #3

skeeter

- 1,103

- 1

captainnumber36 said:

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

The equation for tan(θ - π) is **tan(θ - π) = -tan(θ)**. This means that the tangent of an angle (θ) minus pi (π) is equal to the negative tangent of that angle.

To solve for tan(θ - π), first find the tangent of the angle (θ), then take the negative of that value. This can also be written as **-tan(θ)**.

If tan(θ) = 1, then the value of tan(θ - π) is **-1**. This is because the tangent of an angle is equal to the opposite side divided by the adjacent side of a right triangle, and when the tangent is 1, the two sides are equal in length.

This is due to the periodicity of the tangent function. The tangent function has a period of π, meaning that the values of tan(θ) repeat every π radians. So, tan(θ - π) is simply the same as tan(θ) but shifted π radians to the left, resulting in a negative value.

The equation tan(θ - π) = -tan(θ) can be used in various fields such as engineering, physics, and astronomy. For example, it can be used to calculate the position of an object relative to a reference point, or to determine the distance between two objects. It is also commonly used in trigonometric identities and transformations.

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