Find the size of angle $t$ . Give your answer in degrees $(^{\circ})$ .

Not drawn accurately

Answer

Expert–verified

Hide Steps

Answer

$⌊ t ⌋ = 6$

Steps

Step 1 ： $\cos t = \cos {(\frac{180 t}{π})}^{\circ}$

Step 2 ：Either $t + \frac{180 t}{π} = 360^{\circ} k$ or $t - \frac{180 t}{π} = 360^{\circ} k$

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

Step 4 ：The smallest positive real number of this form is $\frac{360 π}{π + 180}$

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

Step 6 ：The smallest positive real number of this form is $\frac{360 π}{180 - π}$

Step 7 ：Therefore, $t = \frac{360 π}{π + 180} \approx 6.175$

Step 8 ： $⌊ t ⌋ = 6$