Question

Give the exact value of each of the following: 4 cos (-π/4

Answer 1

\[\large \cos(-\theta) = \cos(\theta)\]

Answer 2

\[4\cos( \frac{\pi}{4}) = 4 \times \frac{1}{\sqrt{2}}\]

Answer 3

\[\frac{\pi}{4} = \frac{180}{4} = 45 ^{\circ}\]

Answer 4

\[4\cos( \frac{\pi}{4}) = 4 \times \frac{1}{\sqrt{2}} = \frac{4}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} \implies \frac{4 \sqrt{2}}{2} \implies 2\sqrt{2}\]