basic identities

Question

What is tan Θ when csc Θ= 2√3

Answer 1

cscθ=2*3^.5

csc=1/sin

=1/sin3.464..........

=1/60.4231..........

tanθ=16.5494..........

use atan

θ=86.5422..........

Answer 2

Draw a right triangle with csc Θ = 2√3.

This means hypotenuse is 2√3 and side opposite Θ = 1

The other side then is √11 and the tan Θ = (1/11)sqrt(11).