Question

If tan A = 4/5; what does CSC A =?
Round to nearest tenth.

Answer 1

1.6

Explanation:

`\tan \: A = (4)/(5) \\ \\ \cot \: A = (1)/( \tan \: A ) = (1)/( (4)/(5) ) = (5)/(4) \\ \\ csc\: A = \sqrt{1 + {cot}^(2)\: A} \\ = \sqrt{1 + { \bigg( (5)/(4) \bigg)}^(2) } \\ = \sqrt{1 + (25)/(16) } \\ = \sqrt{(16 + 25)/(16) } \\ = \sqrt{(41)/(16)} \\ = ( √(41) )/(4) \\ = (6.40312424)/(4) \\ = 1.60078106 \\ \therefore \: csc \: A =1.6`