Thread: Evaluating a trigs of trigs

How does one find the value of tan theta that =1/3

I tried to work it out using a triangle and inverse trig functions

If arctan(1/3)=theta then theta = tan(1/3)

that means we should be able to draw a right angle triangle where the side opposte theta is 1 and the side adjacent is 3

this would make the hypotenuse sqrt(10)

however when I use arcsin and arccos to find the angles I get both angles near 18 which would imply that the triangle is not a right triangle.

Am I on the right track at all?

perhaps my calculator should be in radian mode? is that the what im missing? I'm not sure.

Originally Posted by kingsolomonsgrave

How does one find the value of tan theta that =1/3
I tried to work it out using a triangle and inverse trig functions
If arctan(1/3)=theta then theta = tan(1/3)

You have that backwards.
so

Now you have

Evaluate
Hi,
I attached a word-file with the solution.
I hope, does help!
You can verify with the calculator:
tan^-1(0.3333333) =18.434932°
2*tan^-1(0.3333333) =36.869863°
cos(36.869863°) =0.800000
(Use-modus is degree, not radian)

Best regards,
Stefan