Question

if sec(theta)= -3/2, pi < theta < 3pi/2. find the remaining trigonometric ratios?

Answer 1

an now we have a question!

Answer 2

secant is
\[-\frac{3}{2}\]so make a triangle with hypotenuse 3, adjacent 2, solve for the "opposite" side get
\[\sqrt{3^2-2^2}=\sqrt{9-4}=\sqrt{5}\]

Answer 3

now just use ratios being mindful of what quadrant you are in, so you know what is positive and what is negative

Answer 4

\[\cos(\theta)=-\frac{2}{3}\]
\[\sin(\theta)=-\frac{\sqrt{5}}{3}\]
\[\tan(\theta)=\frac{\sqrt{5}}{2}\] etc