Question

find the exact values of the six trigonometric functions of the given angle. do not use a calculator.
240°
select the correct choice below and fill in any answer boxes within your choice.
oa. sin 240°=
(simplify your answer, including any radicals. use integers or fractions for any numbers in th
ob. the function value is undefined.
select the correct choice below and fill in any answer boxes within your choice.
oa. cos 240°=
(simplify your answer, including any radicals. use integers or fractions for any numbers in t
ob. the function value is undefined.
select the correct choice below and fill in any answer boxes within your choice.
oa. tan 240°=
(simplify your answer, including any radicals. use integers or fractions for any numbers in
ob. the function value is undefined.
select the correct choice below and fill in any answer boxes within your choice.

Explanation:

Step1: Find the reference angle

The reference angle of \(240^{\circ}\) is \(240^{\circ}- 180^{\circ}=60^{\circ}\).

Step2: Determine the sign of trigonometric functions

Since \(240^{\circ}\) is in the third quadrant, \(\sin\theta<0\), \(\cos\theta<0\), \(\tan\theta>0\).

Step3: Calculate \(\sin240^{\circ}\)

We know that \(\sin\theta=-\sin(\text{reference angle})\) for \(\theta\) in the third quadrant. So \(\sin240^{\circ}=-\sin60^{\circ}=-\frac{\sqrt{3}}{2}\).

Step4: Calculate \(\cos240^{\circ}\)

We know that \(\cos\theta=-\cos(\text{reference angle})\) for \(\theta\) in the third quadrant. So \(\cos240^{\circ}=-\cos60^{\circ}=-\frac{1}{2}\).

Step5: Calculate \(\tan240^{\circ}\)

We know that \(\tan\theta=\tan(\text{reference angle})\) for \(\theta\) in the third quadrant. So \(\tan240^{\circ}=\tan60^{\circ}=\sqrt{3}\).

Answer:

A. \(\sin240^{\circ}=-\frac{\sqrt{3}}{2}\)
A. \(\cos240^{\circ}=-\frac{1}{2}\)
A. \(\tan240^{\circ}=\sqrt{3}\)