Given that x is measured in radians and x>20, find the smallest value of x such that

Is this an inequality question?

Thanks!!

2. Originally Posted by NyRychVantel
Given that x is measured in radians and x>20, find the smallest value of x such that

Is this an inequality question?

Thanks!!
General solution:

$\cos \left( \frac{x - 1}{3} \right) = - \frac{\sqrt{5}}{4}$

$\Rightarrow \frac{x - 1}{3} = \cos^{-1} \left( - \frac{\sqrt{5}}{4}\right) + 2 n \pi$ or $\frac{x - 1}{3} = \pi + \cos^{-1} \left(\frac{\sqrt{5}}{4}\right) + 2 n \pi$ where n is an integer.

You want the smallest solution for x that is larger than 20.

Of course, if you have access to the appropriate technology you could always use a graph to get the answer .......

3. Originally Posted by mr fantastic
General solution:

$\cos \left( \frac{x - 1}{3} \right) = - \frac{\sqrt{5}}{4}$

$\Rightarrow \frac{x - 1}{3} = \cos^{-1} \left( - \frac{\sqrt{5}}{4}\right) + 2 n \pi$ or $\frac{x - 1}{3} = \pi + \cos^{-1} \left(\frac{\sqrt{5}}{4}\right) + 2 n \pi$ where n is an integer.

You want the smallest solution for x that is larger than 20.

Of course, if you have access to the appropriate technology you could always use a graph to get the answer .......
Please correct me if I'm wrong.

4. Originally Posted by NyRychVantel
Please correct me if I'm wrong.
Correct (assuming accuracy to 1 decimal place is required)