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16 votes
If sin A = 4/5 find the value of cot A + tan A.​

User Rajian
by
7.8k points

2 Answers

8 votes

Answer:

The answer is 2

Explanation:


Cot(x)=(1)/(tan(x)) =(Cos(x))/(Sin(x))


Tan(x) = (Sin(x))/(Cos(x))


Cos((\pi )/(2) -x)=sin(x)

This means that

(\cos \left((\pi )/(2)-(4)/(5)\right))/(\sin \left((4)/(5)\right))+(\sin \left((4)/(5)\right))/(\cos \left((\pi )/(2)-(4)/(5)\right))

This will be a long one to solve
-> apply cos identity to right side


(\cos \left((\pi )/(2)-(4)/(5)\right))/(\sin \left((4)/(5)\right))+(\sin \left((4)/(5)\right))/(\cos \left((\pi )/(2)\right)\cos \left((4)/(5)\right)+\sin \left((\pi )/(2)\right)\sin \left((4)/(5)\right))

-> simplify according to unit circle


(\cos \left((\pi )/(2)-(4)/(5)\right))/(\sin \left((4)/(5)\right))+1

->apply cos identity again


(\cos \left((\pi )/(2)\right)\cos \left((4)/(5)\right)+\sin \left((\pi )/(2)\right)\sin \left((4)/(5)\right))/(\sin \left((4)/(5)\right))+1

If you apply for unit circle numbers,

you will get 2

I do not recommend using a calculator for these questions, but instead, turn the form into
sin(\pi )/(2) other base unit circle locations, and most likely this is the method that your teacher counts as "right."
when using a calculator, it tends to "round" the number, which result in a inaccurate answer

User Eli Stevens
by
8.2k points
2 votes

Answer:

2.08

Explanation:


sin^(-1) 4/5 = 53.13\\tan 53.13 = 1.33\\cot 53.13 = 0.75\\1.33 + 0.775 = 2.08

User Seasong
by
8.1k points

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