9) \\( \\cos \\left( \\frac { - 5 \\pi } { 3 } \\right) \\)\na) 1\nb) \\( \\frac { \\sqrt { 3 } } { 2 }…

9) \\( \\cos \\left( \\frac { - 5 \\pi } { 3 } \\right) \\)\na) 1\nb) \\( \\frac { \\sqrt { 3 } } { 2 } \\)\nc) \\( \\frac { \\sqrt { 2 } } { 2 } \\)\nd) \\( \\frac { 1 } { 2 } \\)

9) \\( \\cos \\left( \\frac { - 5 \\pi } { 3 } \\right) \\)\na) 1\nb) \\( \\frac { \\sqrt { 3 } } { 2 } \\)\nc) \\( \\frac { \\sqrt { 2 } } { 2 } \\)\nd) \\( \\frac { 1 } { 2 } \\)

Answer

Explanation:

Step1: Use the property of cosine function

The cosine function is an even function, i.e., (\cos(-x)=\cos(x)). So, (\cos\left(\frac{-5\pi}{3}\right)=\cos\left(\frac{5\pi}{3}\right)).

Step2: Rewrite the angle

We know that (\frac{5\pi}{3}=2\pi-\frac{\pi}{3}). And (\cos(2\pi - \alpha)=\cos\alpha). So, (\cos\left(\frac{5\pi}{3}\right)=\cos\left(2\pi-\frac{\pi}{3}\right)=\cos\left(\frac{\pi}{3}\right)).

Step3: Find the value

We know that (\cos\left(\frac{\pi}{3}\right)=\frac{1}{2}).

Answer:

D. (\frac{1}{2})