Question

Given $\sin {{60}^{\circ }}=\dfrac{\sqrt{3}}{2}$ and $\cos {{60}^{\circ }}=\dfrac{1}{2}$ , how do you find $\cot {{60}^{\circ }}$ ?

Answer 1

Hint: Here we have been given the value of two trigonometric functions at the same angle and we have to find the value of another trigonometric function with the same angle. Firstly we will write down a relation between the three given functions. Then we will substitute the two values given in that relation. Finally we will solve it to get the value of the third trigonometric function and our desired answer.

Complete step by step answer:
The values given to us are as follows:
$\sin {{60}^{\circ }}=\dfrac{\sqrt{3}}{2}$….$\left( 1 \right)$
$\cos {{60}^{\circ }}=\dfrac{1}{2}$….$\left( 2 \right)$
We have to find the value of the below function:
$\cot {{60}^{\circ }}$
Now as we know that the relation between sine, cosine and cotangent is as follows:
$\cot A=\dfrac{\cos A}{\sin A}$
On substituting $A={{60}^{\circ }}$ in above formula we get,
$\Rightarrow \cot {{60}^{\circ }}=\dfrac{\cos {{60}^{\circ }}}{\sin {{60}^{\circ }}}$
Substitute the value from equation (1) and (2) above we get,
$\Rightarrow \cot {{60}^{\circ }}=\dfrac{\dfrac{1}{2}}{\dfrac{\sqrt{3}}{2}}$
$\Rightarrow \cot {{60}^{\circ }}=\dfrac{1\times 2}{2\times \sqrt{3}}$
Simplifying further we get,
$\Rightarrow \cot {{60}^{\circ }}=\dfrac{1}{\sqrt{3}}$
$\Rightarrow \cot {{60}^{\circ }}=0.577$
So we get the answer as $0.577$
Hence the answer is $\cot {{60}^{\circ }}=0.577$ .

Note:
The six basic trigonometric functions are sine, cosine, tangent, cosecant, secant and cotangent. The last three are inverse functions of the first three functions respectively. Tangent is equal to the ratio of sine to cosine and cotangent is equal to ratio of cosine to sine. There are many identities of trigonometric functions such as the Pythagorean identity, sum and difference identity and many more to solve trigonometric questions.