Question

Find the indicated trig value in the specified quadrant.
Function: cot (x) = -3, quadrant IV, trig value: sin (x)

Answer 1

what are the signs of the cosine and sine in the 4th Quadrant? are they both positive or negative or do they differ?

Answer 2

Sine is negative, and cosine is positive.

Answer 3

\(\bf cot(x) = -3\\ \quad \\ \quad \\
cot(x) = \cfrac{cos(x)}{sin(x)}\quad \textit{therefore}\quad cot(x) = -3\implies cot(x) = -\cfrac{3}{1}\\ \quad \\
\textit{since we're in the 4th Quadrant, sine is negative, thus}\\ \quad \\
cot(x) = -\cfrac{3}{1}\implies cot(x) = \cfrac{3}{-1}\implies \cfrac{a}{b}\\ \quad \\
\textit{to find "c" or the hypotenuse, we can use}\\
c^2 = a^2 + b^2\implies c = \sqrt{a^2+b^2}\\ \quad \\
\textit{keep in mind that }\qquad sin(x) = \cfrac{b}{c}\)