Question

cos 45°
answer
\\(dfrac{1}{2}\\)
\\(dfrac{sqrt{3}}{2}\\)
\\(sqrt{3}\\)
\\(dfrac{sqrt{2}}{2}\\)

Explanation:

Step1: Recall 45-45-90 triangle ratios

In a right isosceles triangle, the adjacent side to 45° and hypotenuse are in ratio $\frac{\sqrt{2}}{2}$.

Step2: Define cosine of an angle

$\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step3: Substitute 45° into cosine formula

$\cos45^\circ = \frac{\sqrt{2}}{2}$

Answer:

$\frac{\sqrt{2}}{2}$