Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable . Tan theta, given that cot theta = radical 11 / 4

Question

What identity best fits the problem to solve?

Answer 1

Let x=theta, then

cotx=(11/4)^1/2 cotangent is adjacent side over opposite side: cotx=a/o

tanx= opposite side over adjacent side. tanx=o/a; o/a=1/(a/o)

tanx=sinx/cosx cotx=cosx/sinx

so, taxx = 1/cotx tangent is just the inverse of the cotangent

IF cotx=(11/4)^1/2 then tanx=1/(4/11)^1/2

11/4=2.75 . square root is 1.658 inverse is 1/1.658= 0.603

Or you could just invert the 11/4 to 4/11 and take the square root: (4/11)^1/2=(.3636)^1/2=0.603

tangent of theta is 0.603

Answer 2

cot is the reciprocal of tan. So cot θ=4/√11. Then, it has to be rationalized.

4/√11 multiply by √11/√11

(4/√11)(√11/√11) Simplify by multiplying across

4√11 /√121 Simplify the radical

cot θ = 4√11/11