## Mirandaregina one year ago 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.

1. phi

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

2. Mirandaregina

@phi yes

3. phi

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)

4. phi

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

5. phi

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

6. Mirandaregina

@phi thank you for explaining this