Question

Given that cosΘ = 1/2 and that Θ lies in quadrant IV, determine the value of tanΘ.

Answer 1

find \(\sin(\theta)\) then tangent is sine over cosine

Answer 2

how do I find sinΘ?

Answer 3

you can find that point on the last page of this cheat sheet
look in quadrant IV where the first coordinate is \(\frac{1}{2}\) and the sine will be the second coordinate
there are other ways to do it, but it is easy to see on the sheet

Answer 4

the other way is to compute \[-\sqrt{1-\left(\frac{1}{2}\right)^2}\]

Answer 5

-√(1+(1/2)^2) = -√5/2

Answer 6

minus, not plus

Answer 7

\[\huge -\sqrt{1\color{red}-\left(\frac{1}{2}\right)^2}\]

Answer 8

AB^2 = OB^2 - OA^2
= 2^2 - 1^2


= 4-1
=3
\[AB=-\sqrt{3}\]

Answer 9

unit circle cheat sheet is very helpful here

Answer 10

\[TAN \theta = \frac{ AB }{ OA }\]

Answer 11

Thanks!