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.
no way!
sinx x has to be a value between -1 and +1, can't be 2
since cot x = 1/2 ---> opposite = 2, adjacent = 1
construct a triangle with sides 1 and 2, the hypotenuse then is √5
cosx = 1/√5
sinx = 2/√5
(1) False. This is not a possible situation.
(2) In the first quadrant, both the cosine and sine values of an angle are positive. In this case, if cot x = 1/2, it means that cos x / sin x = 1/2. To find cos x and sin x, we can use the equation cot x = cos x / sin x.
Dividing both sides of the equation by cos x, we get:
cos x / cos x / sin x = 1/2
1 / sin x = 1/2
1 = sin x / 2
This equation tells us that sin x = 2, which is not possible in the first quadrant since the maximum value for sin x is 1. Therefore, the given situation is not possible.