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 Question from Ruby, a student: Given that tan x= cos 100 and x=0-180. calculate the value of x. (All measurements in degrees)

Ruby,

I presume you mean that x is in the interval [0°,180°]? Please don't use the equals sign except to express that the things on opposite sides of it are equal! It leads to confusion.

There is no "tidy" answer to this. Even cos(100) is very messy, involving an irrational root of a cubic equation; and there are not as far as I know any identities that will help out here.

There is a related class of problems you CAN solve. If you had wanted to solve [say] arctan(x) = arccos(0.5) you could do so by labelling the sides of a right triangle so the cosine of the angle is (0.5) - eg, hypotenuse = 1, adjacent side 0.5; thus opposite side = ?; tangent = ?.

You will just have to evaluate arctan(cos(100)); Google can do this for you.

Good Hunting!
RD

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