Year 11 Maths - Specialist Circular functions

Symmetry properties and the Pythagorean identity

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Questions

Question 1

21012

Evaluate $\cos \left( { - \frac{{17\pi }}{3}} \right)$

Answer

$ - \frac{1}{2}$

Worked Solution

$$
\begin{aligned}
\cos \left(-\frac{17 \pi}{3}\right)&=\cos \left(\frac{17 \pi}{3}\right)\\
&=\cos \left(5 \pi+\frac{\pi}{3}\right) \\
&=\cos \left(4 \pi+\left(\pi+\frac{\pi}{3}\right)\right) \\
&=\cos \left(\pi+\frac{\pi}{3}\right) \\
&=-\cos \frac{\pi}{3}=-\frac{1}{2}
\end{aligned}
$$

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