Why Tan θ = sin θ / cos θ

Frequently in math, when it comes to trigonometry, a lot of people know that Tan θ = sin θ / cos θ, but do you actually know why this concept is logical?

Let’s take a look at this triangle inside of the semi circle.

The triangle has a hypotenuse of the same length as that of the radius of the circle. We represent the opposite side of θ as y (the vertical axis) and the adjacent side as x (the horizontal axis). With that we can find cos θ and sin θ using x and y .

SOH CAH TOA

Sin θ = Opposite / Hypotenuse = y / 1 = y

Cos θ = Adjacent / Hypotenuse = x / 1 = x

Tan θ = Opposite / Adjacent = y / x = sin θ / cos θ

 

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