Question

evaluate: cos 600°

Explanation:

Step1: Reduce the angle

Since \(600^{\circ}=360^{\circ} + 240^{\circ}\), then \(\cos600^{\circ}=\cos(360^{\circ}+ 240^{\circ})\). According to the periodicity of the cosine function \(\cos(A + 360^{\circ})=\cos A\), so \(\cos(360^{\circ}+240^{\circ})=\cos240^{\circ}\).

Step2: Use the angle - transformation formula

\(240^{\circ}=180^{\circ}+60^{\circ}\), and \(\cos(A + 180^{\circ})=-\cos A\). So \(\cos240^{\circ}=\cos(180^{\circ}+60^{\circ})=-\cos60^{\circ}\)

Step3: Calculate the value of \(\cos60^{\circ}\)

We know that \(\cos60^{\circ}=\frac{1}{2}\)

Answer:

\(-\frac{1}{2}\)