trig
posted by Keenia on .
Find the exact value of the trigonometric function. cot(pi/4 + 16pi)

16π is the same as exactly 8 rotations, so
cot(π/4 + 16π) = cot(π/4)
= 1/tan(π/4) = 1/1 = 1 
cot ( A + B ) = 1 / tan ( A + B )
tan ( A + B )= ( tanA + tanB )/( 1  tanA * tanB )
In this case:
A = pi / 4
B = 16 pi
tan ( pi / 4 ) = tan 45° = 1
tan ( 16 pi )= cot ( 8 * 2 pi ) = tan ( 8 * 360° ) = 0
tan ( pi / 4 + 16 pi ) =
[ ( tan ( pi / 4 ) + tan ( 16 pi ) ]/[ 1  tan( pi / 4 ) * tan ( 16 pi ) ] =
( 1 + 0 ) / ( 1  1 * 0 ) =
1 / ( 1  0 ) =
1 / 1 = 1
tan ( pi / 4 + 16 pi ) = 1
cot ( pi / 4 + 16 pi ) =
1 / tan ( pi / 4 + 16 pi ) =
1 / 1 = 1
 cot ( pi / 4 + 16 pi ) =  1 
tan ( 16 pi )= tan ( 8 * 2 pi ) = tan ( 8 * 360° ) = 0