Question

find the exact values of the six trigonometric functions of the given angle. do not use a calculator. 300°. select the correct choice below and fill in any answer boxes within your choice. sin 300° = -\frac{\sqrt{3}}{2} (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) a. the function value is undefined. b. the function value is -\frac{\sqrt{3}}{2} cos 300° = \frac{1}{2} (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) a. the function value is undefined. b. the function value is \frac{1}{2} tan 300° = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) a. tan 300° = b. the function value is undefined

Explanation:

Step1: Rewrite the angle

$300^{\circ}=360^{\circ}- 60^{\circ}$.

Step2: Find $\sin300^{\circ}$

Using the property $\sin(A - B)=\sin A\cos B-\cos A\sin B$ or the unit - circle property $\sin(360^{\circ}-\alpha)=-\sin\alpha$, we have $\sin300^{\circ}=\sin(360^{\circ}-60^{\circ})=-\sin60^{\circ}=-\frac{\sqrt{3}}{2}$.

Step3: Find $\cos300^{\circ}$

Using the property $\cos(360^{\circ}-\alpha)=\cos\alpha$, we get $\cos300^{\circ}=\cos(360^{\circ}-60^{\circ})=\cos60^{\circ}=\frac{1}{2}$.

Step4: Find $\tan300^{\circ}$

Since $\tan\theta=\frac{\sin\theta}{\cos\theta}$, then $\tan300^{\circ}=\frac{\sin300^{\circ}}{\cos300^{\circ}}=\frac{-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=-\sqrt{3}$.

Answer:

$\sin300^{\circ}=-\frac{\sqrt{3}}{2}$, $\cos300^{\circ}=\frac{1}{2}$, $\tan300^{\circ}=-\sqrt{3}$