find the exact values of the six trigonometric functions of the given angle. do not use a calculator.\n240°\n…
find the exact values of the six trigonometric functions of the given angle. do not use a calculator.\n240°\nselect the correct choice below and fill in any answer boxes within your choice.\noa. sin 240°=\n(simplify your answer, including any radicals. use integers or fractions for any numbers in th\nob. the function value is undefined.\nselect the correct choice below and fill in any answer boxes within your choice.\noa. cos 240°=\n(simplify your answer, including any radicals. use integers or fractions for any numbers in t\nob. the function value is undefined.\nselect the correct choice below and fill in any answer boxes within your choice.\noa. tan 240°=\n(simplify your answer, including any radicals. use integers or fractions for any numbers in\nob. the function value is undefined.\nselect the correct choice below and fill in any answer boxes within your choice.
Answer
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})