Question

Write cos11π18 in terms of the cosine of a positive acute angle.

Answer 1

The expression for cos(11π/18) in terms of the cosine of a positive acute angle is -cos(7π/18).

Step-by-step explanation:

To express cos(11π/18) in terms of the cosine of a positive acute angle, we must find an acute angle α such that cos(11π/18) = cos(α). Since 11π/18 is greater than π/2 but less than π, it is in the second quadrant, where cosine is negative. However, the reference angle for 11π/18 in the second quadrant is π - 11π/18, which is 7π/18. This is an acute angle, and the cosine function is even, so cos(11π/18) = cos(π - 7π/18) = -cos(7π/18). Therefore, cos(11π/18) in terms of the cosine of a positive acute angle is -cos(7π/18).

Answer 2

An Angle is said to be Acute , if it lies between 0° to 90°.

In terms of Radian

`\rightarrow 0\leq \text{Angle} < (\pi)/(2)\\\\ \rightarrow \cos (11\pi )/(18)\\\\=\cos(\pi -(7\pi)/(18))\\\\=-\cos( (7\pi)/(18))`

⇒Cos(π-A)= -Cos A, becuse cosine of An Angle is Negative in Second Quadrant.