Problem

Find the size of angle $t$. Give your answer in degrees $\left(^{\circ}\right)$. Not drawn accurately

Solution

Step 1 :\(\cos t = \cos \left( \frac{180t}{\pi} \right)^\circ\)

Step 2 :Either \(t + \frac{180t}{\pi} = 360^\circ k\) or \(t - \frac{180t}{\pi} = 360^\circ k\)

Step 3 :From the first equation, \(t = \frac{360^\circ \pi k}{\pi + 180}\)

Step 4 :The smallest positive real number of this form is \(\frac{360 \pi}{\pi + 180}\)

Step 5 :From the second equation, \(t = \frac{360^\circ \pi k}{\pi - 180}\)

Step 6 :The smallest positive real number of this form is \(\frac{360 \pi}{180 - \pi}\)

Step 7 :Therefore, \(t = \frac{360 \pi}{\pi + 180} \approx 6.175\)

Step 8 :\(\lfloor t \rfloor = \boxed{6}\)

From Solvely APP
Source: https://solvelyapp.com/problems/8074/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download