Why is cos(0) = 1?

2 Answers
Jun 28, 2015

In terms of the right triangles used to define trigonometric functions, #cos(x) = frac{"adjacent side"}{"hypotenuse"}#. When #x=0#, #"adjacent side length" = "hypotenuse length"#. Therefore, #cos(0) = 1#.

Explanation:

Consider a series of triangles with the base angle gradually approaching the value 0.

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Feb 20, 2018

We can use the Unit Circle to prove this to ourselves:

Explanation:

https://en.wikipedia.org/wiki/Unit_circle

At #0# degrees, the angle intercepts the Unit Circle at the coordinate #(1,0)#. The coordinates are the trig values. The x-coordinate is the #cos# value and the y-coordinate is the #sin# value.