Why does cosine of zero equal one

The cosine of angle zero degrees can be derived in three mathematical approaches but two methods are related to geometric system and the remaining one is related to trigonometry.

In this method, we consider a property between sides of a triangle for proving the exact value of cosine of angle zero degrees. According to the definition of the cos function , express it in ratio form in terms of lengths of the sides.

In a zero degree right triangle, the lengths of both adjacent side and hypotenuse are equal because the length of the opposite side is equal to zero. The cos of angle zero degrees can also be proved practically by constructing a right triangle with zero degrees angle. You need to find some definition of the trigonometric functions which does not rely only on right-angled triangles there are several conventional approaches, both geometric, algebraic and analytic, and most reasonable approaches give the same result in the end.

Add a comment. Active Oldest Votes. Karl Karl 4, 4 4 gold badges 15 15 silver badges 23 23 bronze badges. In any case, the key point here is this: When doing classical trigonometry, in normal case but definitely also in "extreme" cases, you need to define adjacent side and opposite side in such a way that either of them can never be the hypotenuse.

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Email Required, but never shown. Upcoming Events. Featured on Meta. As you already know, trigonometric functions refer to angular functions that relate the angles of a triangle. For studying periodic phenomena of light and sound waves, trigonometric functions have been used. These functions are also crucial for studying the harmonic oscillation and average temperature variations.

The cosine function of an angle follows a particular formula. According to this formula, the value of a cosine function of an angle is the length of the adjacent side divided by the length of the hypotenuse side.

The formula is written below.