Why is cos(0) = 1?

2 Answers
Alan P. ยท Anjali G
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.

enter image source here

Jacobi J.
Feb 20, 2018

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

Explanation:

![https://en.wikipedia.org/wiki/Unit_circle](useruploads.socratic.org)

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.

Related questions
See all questions in Trigonometric Functions of Any Angle
Impact of this question
170924 views around the world
You can reuse this answer
Creative Commons License