Question

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

Explanation:

Step1: Rewrite the angle

$300^{\circ}=360^{\circ}- 60^{\circ}$. In the fourth - quadrant, tangent, sine and cosecant are negative, and cosine and secant are positive.

Step2: Find $\tan300^{\circ}$

$\tan300^{\circ}=\tan(360^{\circ}-60^{\circ})=-\tan60^{\circ}=-\sqrt{3}$, so the correct choice for $\tan300^{\circ}$ is A.

Step3: Find $\csc300^{\circ}$

$\csc300^{\circ}=\csc(360^{\circ}-60^{\circ})=-\csc60^{\circ}=-\frac{2\sqrt{3}}{3}$, so the correct choice for $\csc300^{\circ}$ is A.

Step4: Find $\sec300^{\circ}$

$\sec300^{\circ}=\sec(360^{\circ}-60^{\circ})=\sec60^{\circ}=2$, so the correct choice for $\sec300^{\circ}$ is A.

Answer:

For $\tan300^{\circ}$: A. $-\sqrt{3}$
For $\csc300^{\circ}$: A. $-\frac{2\sqrt{3}}{3}$
For $\sec300^{\circ}$: A. $2$