Some Applications Of Trigonometry

Question

Given $space secθ space equals space 13 over 12 comma space$ calculate all other trigonometric ratios.

Solution

Let us draw a right angle triangle, right angled at B.
We know that:

secθ space equals space 13 over 12 equals AC over AB

Let AB = 12 K, AC = 13K
where K is a positive number.
WiredFaculty

Using Pythagoras theorem, we have
AC² = AB² + BC²⇒(13 K)² = (12 K)² + BC²⇒169 K² = 144 K² + BC²⇒BC² = 169 K²-144 K²BC² = 25 K² $rightwards double arrow$ BC = 5 K.
Now,
WiredFaculty
and $cosecθ space equals space AC over BC equals fraction numerator 13 straight K over denominator 5 straight K end fraction equals 13 over 5.$