Question

What is the exact value of the trigonometric expression? Cos (16rad/3)

Answer 1

Hence, the value of given expression is: 0.581797

Explanation:

We know that
`(22)/(7) \textradian=180degree=\pi radian`

This means

`1 \textradian=(180 * 7)/(22)degree`

`(16)/(3) radian=((180 * 16* 7 )/(22* 3)) degree=305.577degree`

Hence,
`(16)/(3)\text rad=305.577degree`

Hence,
`\cos (305.577\degree)=0.581797`

Hence, the value of given expression is: 0.581797

Answer 2

Given the trigonometric expression:
`\cos((16 \pi)/(3))`

we can rewritten expression

`\cos((16 \pi)/(3))` as

`\cos ((12+4)/(3) \pi)` =
`\cos(((12)/(3)+(4)/(3)) \pi)` =
`\cos (2\pi \cdot 2 + (4 \pi)/(3))`

Using the periodicity of cosine:

`\cos (x+2\pi \cdot k) = \cos x`

we get;

`\cos(4 \pi)/(3)`

write this as:

`\cos((4\pi)/(3)) = \cos(\pi + (\pi)/(3))`

Also:
`\cos(\pi +x) = -\cos(x)`

then we get;

`-\cos((\pi)/(3)})`

=
`-(1)/(2)`

Therefore, the exact value of the given trigonometric expression is;
`-(1)/(2)`