Question

What is cos 45 degrees in simplified radical form?​

Answer 1

Answer:

The value of cos 45 degrees in simplified radical form is 0.70710 approximately.

Solution:

Given, Cos of angle 45 degrees.

We have to find the value of the Cos of 45 degrees in radical form.

From trigonometric ratios,  

Cos of angle 45 degrees = cos ⁡45 = $\frac{1}{\sqrt{2}}$

Multiplying numerator and denominator with square root of 2

$\begin{array}{l}{=\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}} \\\\ {=\frac{1 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}}} \\\\ {=\frac{\sqrt{2}}{(\sqrt{2})^{2}}} \\\\ {=\frac{\sqrt{2}}{2}}\end{array}$

The value of square root of 2 is 1.414213

$=\frac{1.414213}{2}=0.70710$

Hence, the value of Cos of angle 45 degrees is 0.70710 approximately