Expert: Ahmed Salami - 7/10/2011

Question
Given that cosec A= 7/2, where 90 degrees < A < 180 degrees.

Find the exact value of

i. sec A
ii. tan A

Answer
Hi Sarah,
If cosec A = 7/2, then sin A = 2/7
Using the identity;
sin²A + cos²A = 1
cos A = √(1 - sin²A)
= √(1 - (2/7)²)
= √(1 - (4/49))
= √(45/49)
=  ±(√45)/7
but cos A < 0 for all 90° < A < 180°
So, cos A = -(√45)/7, and
i) sec A = -7/√45 = -(7√45)/45

ii) tan A = sin A/cos A
= -2/√45
= -(2√45)/45

Regards