Question

Why do we use cosine?

Answer 1

In the given question, we have been asked to use the cosine function. The cosine is one of the functions of the trigonometry and in the right angled triangle it is equal to the ratio of the adjacent side to the hypotenuse. In order to answer the cosine, we will need to tell the uses of the rules of cosine.

Complete step by step solution:
Cosine function i.e. $\cos \theta$ tells us the shape of a right angle triangle.
Let us consider the triangle ABC right angled at B

We know that:
$\cos \theta =\dfrac{base}{hypotenuse}$
The cosine function of a trigonometry is used to solve a only right angled triangle i.e. rule of a cosine function is used when either we have been given all the three sides of the triangle or we have given the measure of only two sides of a triangle and the angle included in between two lines.
Cosine function is used to relate all the sides of a right-angled triangle to the given one angle of a triangle:
Cosine rule for finding the side is ${{a}^{2}}={{b}^{2}}+{{c}^{2}}-2bc\cos \left( A \right)$ , where ‘a’ is the side that to be find, b and c are the given sides and, ‘A’ is the angle that is given and opposite to the side ‘a’.
Cosine rule for finding the angle is $\cos \left( A \right)=\dfrac{{{b}^{2}}+{{c}^{2}}-{{a}^{2}}}{2bc}$ , where ‘a’, b and c are the given sides and, ‘A’ is the angle that is to find and opposite of the side ‘a’.

Note : The cosine graph or the cos function graph is an up-down graph. Cosine is the one the three important and basic functions of trigonometry. There are many identities and formulas based on the cosine that is formed in trigonometry that can help in finding different values of different functions. The range of the cosine function is from -1 to 1.