 # Tangent and the graph of tan(x)

Note by , created almost 6 years ago

## This note gives a definiton of tangent of an angle, and explains the shape of the y = tan(x) graph 165 3 0  Created by rory.examtime almost 6 years ago
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### Page 1

In a right-angled triangle, the tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

﻿﻿﻿﻿﻿﻿tan(x) = O﻿ = ﻿Sin(x)﻿﻿﻿﻿﻿              A     Cos(x)

For example, in this triangle:

the tangent of A (tanA) is ﻿1.33﻿﻿, because the ratio of th opposite side(4) to the adjacent side(3) is 4/3.

﻿﻿Graph of tan(x):

- Tan(x) has vertical asymptotes at values where cos(x) = 0, as the tangent is undefined for these values (cannot divide by zero).

-Tan(x) has a period of π

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