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. a. sin 300° = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) b. the function value is undefined. hw score: 57.14%, 8 of 14 points. question 9, 5.2.49. part 1 of 6. points: 0 of 1. save

Explanation:

Step1: Rewrite the angle

We know that $300^{\circ}=360^{\circ}- 60^{\circ}$. So, $\sin300^{\circ}=\sin(360^{\circ}-60^{\circ})$.

Step2: Apply the sine - angle formula

According to the formula $\sin(A - B)=\sin A\cos B-\cos A\sin B$, when $A = 360^{\circ}$ and $B = 60^{\circ}$, $\sin(360^{\circ}-60^{\circ})=\sin360^{\circ}\cos60^{\circ}-\cos360^{\circ}\sin60^{\circ}$. Since $\sin360^{\circ}=0$ and $\cos360^{\circ}=1$, we have $\sin(360^{\circ}-60^{\circ})=0\times\cos60^{\circ}-1\times\sin60^{\circ}$.

Step3: Find the value of $\sin60^{\circ}$

We know that $\sin60^{\circ}=\frac{\sqrt{3}}{2}$. So, $\sin(360^{\circ}-60^{\circ})=-\frac{\sqrt{3}}{2}$.

Answer:

$\sin300^{\circ}=-\frac{\sqrt{3}}{2}$