Question 942396: If cosine is 2/5, find sin and tan.
Any help on how to do this? Thanks!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! cosine is equal to 2/5
cosine is positive in quadrants 1 and 4.
since cosine is equal to adjacent / hypotenuse, then you can solve for opposite using pythagorus formula of a^2 + b^2 = c^2.
let a = 2 and c = 5
formula of a^2 + b^2 = c^2 becomes 2^2 + b^2 = 5^2.
solve for b^2 to get b^2 = 5^2 - 2^2 = 25 - 4 = 21.
this makes b = plus or minus sqrt(21)
a is the side adjacent which is 2.
b is the side opposite which is plus or minus sqrt(21).
c is the hypotenuse which is 5.
in quadrant 1, side opposite is positive so side opposite is equal to sqrt(21).
in quadrant 4, side opposite is negative so side opposite is equal to -sqrt(21).
hypotenuse of 5 is always positive.
side adjacent is always equal to 2 in both quadrants 1 and 4.
sine is equal to side opposite divided by hypotenuse.
this makes sine equal to sqrt(21)/5 in quadrant 1 and -sqrt(21)/5 in quadrant 4.
tangent is equal to side opposite divided by side adjacent.
this makes tangent equal to sqrt(21)/2 in quadrant 1 and -sqrt(21)/2 in quadrant 4.
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