## Tan Graph – y=tan(x)

The graph of y=tanx is different from the other cos and sin graphs as it has a range from -∞ to ∞ and a period of 180° or π radians. The graph of y=tan(x) in radians is shown below

As can be seen from the graph the curve passes through the origin. It has vertical asymtopes (lines it tends toward but never touches — in this case where the graph goes to infinity) at x =π/2,3π/2,5π/2 and x=-π/2,-3π/2 etc radians or at x=90,270,450 and x=-90,-270 etc degrees.

The graph has a stationary (flat) point whenver it crosses the x-axis.

## Trigonometry: Sin, Cos and Tan

This is the basics of using sine, co-sine and tangent for a right angled triangle. To do this you’ll probably need a scientific calculator

To perform calculations we are going to use the triangle above.

The three main relationships are:

Tan(x) = o/a

Sin(x) = o/h

Cos(x) = a/h

so if h = 5 and x = 30

a = Cos(30)h = 4.330

We can also use a **inverse** of the functions

ie) x = tan^{-1}(o/a)

x = sin^{-1}(o/h)

x = cos^{-1}(a/h)

so if o = 5 and a = 10

x = tan^{-1}(5/10) = 26.565

Using this information we can work out any side or angle in a right angled triangle as long as we have to other pieces of information (like a side and a angle or 2 sides). This is used a lot in resolving forces in physics and allows us to derive some other more complex equations.

Soon ill be adding a maths section to my site Breakingwave

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