Find the exact value of the given trignometric function Do n

Find the exact value of the given trignometric function. Do not use a calculator. -cot(pi/4 + 18 pi) -cot(pi/4 + 18 pi) =

given question is - cot ( /4 + 18 )

now to find this value

1st quadrant is 0 to /2

2nd quadrant is /2 to

3rd quadrant is to 3/2

4th quadrant is 3/2 to 2

these 4 quandrants will be repeating after 2

now 18 = 9 * 2

that means we have fully 9 rotations

after this we are in 1st quadrant and in this all trigonametric functions are positive

so - cot ( /4 + 18 ) = - cot(/4)

but cot(/4) =1

so - cot ( /4 + 18 ) = - 1 (Answer)

the value of - cot ( /4 + 18 ) is -1

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