Hello, I'm currently studying for an exam I will have right before semester 2 starts now in August and I could really use some help
The question is basically "Calculate the value of tan(cos^-1(0.5))"
I can't understand why or how I would do this, do I turn cosinus into something using sinus and tangens or where do I begin??
Thank you!
tan(x)= sin(x)/cos(x) so tan(arcos(x))= sin(arcos(x))/cos(arcos(x)). The denominator is just cos(arcos(x))= x. For the numerator, so that and . The sign is the sign on x itself.
A less "rigorous" way to do this is to imagine a right triangle with hypotenuse of length 1 and "near side" of length x (so that the cosine of the angle is x/1= x). By the Pythagorean theorem the "opposite side" has length . tangent is "opposite side over near side" so . Again, if you are allowing angles outside 0 to [itex]\pi/2[/itex], you will need to check the sign.