Given $csctheta^circ=sqrt3/2$ and $sectheta^circ=sqrt3/3$ , how do you find $sec(90^circ-theta)$ ?

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Answer 1 · 2016-12-19T05:53:14

There is no solution.

$sin theta = 1/(csc theta)$

$sin theta = 2/sqrt3 = 2/1.73$

$= 1.15 > 0$

Therefore, there is no such angle $theta$ that has sin > 1.

Answer 2 · 2016-12-19T07:11:33

There is no such angle $theta$ and we do not have a solution.

As the trigonometric ratios cosecant and secant cannot have their absolute value less than one

i.e. $|csctheta|>=1$ and $|sectheta|>=1$

However, here $csctheta=sqrt3/2=1.732/2=0.866<1$

and $sectheta=sqrt3/3=1.732/3=0.5773<1$

There is no such angle $theta$ and we do not have a solution.

Given csctheta^circ=sqrt3/2csctheta^circ=sqrt3/2 and sectheta^circ=sqrt3/3sectheta^circ=sqrt3/3, how do you find sec(90^circ-theta)sec(90^circ-theta)?