Question #f46bb

1 Answer
Oct 27, 2017

secβ=355

Explanation:

Using standard identities, secβ=1cosβ=±11sin2β
Substituting in sinβ=23
sin2β=49
1sin2β=59
±1sin2β=±53=cosβ
Since β is in the third quadrant, both sinβ and cosβ are negative, we need cosβ=53
So secβ=1cosβ=153=35,
which might also be written, with a rational denominator, as:
secβ=355