SOLUTION: If tan β = 4/5 then, without a calculator, find tan(𝛑/2 - β). Write your answer as a fraction please. Thank You

Algebra ->  Trigonometry-basics -> SOLUTION: If tan β = 4/5 then, without a calculator, find tan(𝛑/2 - β). Write your answer as a fraction please. Thank You      Log On


   

Question 1145658: If tan β = 4/5 then, without a calculator, find tan(𝛑/2 - β). Write your answer as a fraction please.
Thank You
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The formula for the tangent of the difference of two angles, namely:



fails us in this instance because is undefined. Pity.

However, recall that , hence



So:











Similarly,



Now we can use the difference formulas for sine and cosine to calculate



And



Since , the signs of sine and cosine must be the same.





And





Then





John

My calculator said it, I believe it, that settles it