Since cot x = cos x / sin x, if cot x = 1/2, with the angle x in the first quadrant,
then cos x = 1 and sin x = 2
(1) State true or false. Is this a possible situation?
(2) If false, explain why.
2 answers
the values for sine and cosine are limited to the range ±1
cot x = 1/2 can be written in an infinite number of ways, the 1/2 is simply the ratio expressed in simplest form
how about cot x = .5/1
or how about cotx = .378/.756
etc
by definition cotx = adjacent side/opposite side
in a right-angled triangle
so in the original given cotx = 1/2
the adjacent is 1, and the opposite is 2,
or x = 1 and y = 2
r^2 = 1^2 + 2^1 = 5
r = √5
then sinØ = 2/√5 and cosØ = 1/√5
then tanØ = (2/√5) / (1/√5) = 2/1
and cotØ = 1/2
how about cot x = .5/1
or how about cotx = .378/.756
etc
by definition cotx = adjacent side/opposite side
in a right-angled triangle
so in the original given cotx = 1/2
the adjacent is 1, and the opposite is 2,
or x = 1 and y = 2
r^2 = 1^2 + 2^1 = 5
r = √5
then sinØ = 2/√5 and cosØ = 1/√5
then tanØ = (2/√5) / (1/√5) = 2/1
and cotØ = 1/2