Question

Question in attachment

Answer 1

Answer:

$cos(x)=-\frac{\sqrt{3} }{2}$

$sin(x)=\frac{1}{2}$

$tan(x)=-\frac{1}{\sqrt{3} }$

$csc(x)=2$

$sec(x)=-\frac{2}{\sqrt{3}}$

$cot(x)=-\sqrt{3}$

Step-by-step explanation:

(I'll just use x for ease of writing)

We have the trig equation $cos(x)=-\frac{\sqrt{3} }{2}$, and we know that its terminal side is in the 2nd quadrant. By using a unit circle, we can determine that the angle is $\frac{5\pi}{6}$ which has an ordered pair of $(-\frac{\sqrt{3} }{2},\frac{1}{2} )$

$sin(x)=y$, so $sin(x)=\frac{1}{2}$

$tan(x)=\frac{y}{x}$, so $tan(x)=\frac{\frac{1}{2} }{-\frac{\sqrt{3} }{2} }=-\frac{1}{\sqrt{3} }$

Now that we have sin, cos, and tan, we can just take the reciprocal of each of these to get our answers for csc, sec, and cot.

$csc(x)=\frac{1}{sin(x)}$, so $csc(x)=2$

$sec(x)=\frac{1}{cos(x)}$, so $sec(x)=-\frac{2}{\sqrt{3}}$

$cot(x)=\frac{1}{tan(x)}$, so $cot(x)=-\sqrt{3}$

Answer 2

Step-by-step explanation: