Question

If sec (π/2 – theta) = (√3)/2, what is csc theta?

So far I have that theta = (π - √3)/2, but I don’t know how to use that to find csc theta.

Answer 1

are you sure it says sqr(3)/2 and not 2/sqr(3) ?

Answer 2

@phi yes

Answer 3

sec is 1/cos
sec(90-x) = 1/cos(90-x)

cos(90-x) = cos(90)cos(x) + sin(90)sin(x) = 0+1*sin(x)= sin(x)
so sec(90-x)= 1/sin(x)

Answer 4

so we are told
\[ \frac{1}{\sin(x)}= \frac{\sqrt{3}}{2} \\
\sin x = \frac{2}{\sqrt{3}} \]
the problem is 2/sqrt(3) is about 1.1547
and the max sin can ever be is 1

Answer 5

however, if we ignore that detail
then
\[ \frac{1}{\sin(x)}= \csc(x)= \frac{\sqrt{3}}{2} \]
and the answer is sqr(3)/2

Answer 6

@phi thank you for explaining this