SOLUTION: If tan(theta)=4 find the exact values of a) sec^2(theta) b) cot(theta) c) cot(pi/2-theta) d) csc^2(theta)

Algebra ->  Trigonometry-basics -> SOLUTION: If tan(theta)=4 find the exact values of a) sec^2(theta) b) cot(theta) c) cot(pi/2-theta) d) csc^2(theta)      Log On


   

Question 608766: If tan(theta)=4 find the exact values of a) sec^2(theta) b) cot(theta) c) cot(pi/2-theta) d) csc^2(theta)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
If tan(theta)=4 find the exact values of a) sec^2(theta) b) cot(theta) c) cot(pi/2-theta) d) csc^2(theta)
**
For [0,π/2]
use x for theta
If tan x=4=opposite side/adjacent side=4/1
hypotenuse=√(4^2+1^2)=√(16+1)=√17
a) sec^2x=(√17)/1)^2=17
b)cotx=1/4
c)cot(π/2-x) =tanx=4
d) csc^2x=(√17/4)^2=17/16