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natita [175]
2 years ago
11

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

Mathematics
1 answer:
ZanzabumX [31]2 years ago
6 0

Answer:

1.6

Step-by-step explanation:

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

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