Answer:
Given the trigonometric expression: [tex]\cos(\frac{16 \pi}{3})[/tex]
we can rewritten expression
[tex]\cos(\frac{16 \pi}{3})[/tex] as
[tex]\cos (\frac{12+4}{3} \pi)[/tex] = [tex]\cos((\frac{12}{3}+\frac{4}{3}) \pi)[/tex] = [tex]\cos (2\pi \cdot 2 + \frac{4 \pi}{3})[/tex]
Using the periodicity of cosine:
[tex]\cos (x+2\pi \cdot k) = \cos x[/tex]
we get;
[tex]\cos\frac{4 \pi}{3}[/tex]
write this as:
[tex]\cos(\frac{4\pi}{3}) = \cos(\pi + \frac{\pi}{3})[/tex]
Also: [tex]\cos(\pi +x) = -\cos(x)[/tex]
then we get;
[tex]-\cos(\frac{\pi}{3}})[/tex]
=[tex]-\frac{1}{2}[/tex]
Therefore, the exact value of the given trigonometric expression is; [tex]-\frac{1}{2}[/tex]
Answer:
Hence, the value of given expression is: 0.581797
Step-by-step explanation:
We know that [tex]\dfrac{22}{7} \textradian=180degree=\pi radian[/tex]
This means
[tex] 1 \textradian=\dfrac{180 \times 7}{22}degree[/tex]
[tex]\dfrac{16}{3} radian=(\dfrac{180 \times 16\times 7 }{22\times 3}) degree=305.577degree[/tex]
Hence, [tex]\dfrac{16}{3}\text rad=305.577degree[/tex]
Hence, [tex]\cos (305.577\degree)=0.581797[/tex]
Hence, the value of given expression is: 0.581797
