Question

Find the indicated trigonometric value in the specified quadrant.
Function: cot θ = -2
Quadrant: IV
Trigonometric Value ; sin θ

Answer 1

draw a picture



find h using pythagoras's theorem h^2 = 1^1 + 2^2

\[h = \sqrt{5}\]

4th quadrant sin is negative

then \[\sin \theta = \frac{-1}{\sqrt{5}}\]

Answer 2

so i multiply top and bottom by √5. and get

Answer 3

oops cot = 1/tan so \[\tan \theta = -\frac{1}{2}\]

Answer 4

i got -√5/5 as my final answer, does this look right?

Answer 5

if you want to rationalize the denominator

the answer will be

\[\sin \theta = -\frac{\sqrt{5}}{5}\]