Question

find the exact value of $sec 240^circ$ in simplest form with a rational denominator.

Explanation:

Step1: Recall secant definition

$\sec\theta = \frac{1}{\cos\theta}$
So $\sec240^\circ = \frac{1}{\cos240^\circ}$

Step2: Find reference angle of $240^\circ$

$240^\circ - 180^\circ = 60^\circ$, $\cos240^\circ = -\cos60^\circ$

Step3: Substitute $\cos60^\circ$ value

$\cos60^\circ = \frac{1}{2}$, so $\cos240^\circ = -\frac{1}{2}$

Step4: Calculate $\sec240^\circ$

$\sec240^\circ = \frac{1}{-\frac{1}{2}} = -2$

Answer:

$-2$