Question

Find the exact value of y
1.) y=tan^-1 (tan 3pi/4)
2.) y=cos^-1 (cos7pi/6)
3.) y=cos(sin^-1 1/2)

Answer 1

a simple solution is to draw out the triangles

Answer 2

the inverses cancel out each other when they are the same base function; but the angle changes to fit the range of the inverse

Answer 3

if i recall correctly tan and cos inverses are on top of the circle (0 to pi); and sin is on the side (-pi/2 to pi/2)

Answer 4

Actually, they are all special angles...
1.) y=tan^-1 (tan 3pi/4) = 1=tan^-1 (-tan (pi/4)) = tan^-1 (-1) = 3pi/4 or7pi/4
2.) y=cos^-1 (cos7pi/6) = cos^-1 (-cos pi/6) = 5pi/6 or 7pi/6
3.) y=cos(sin^-1 1/2) = cos (pi/6) or cos (5pi/6) = sqrt(3) / 2 or - sqrt(3) / 2

Answer 5

the inverses are one to one, so they dont give 2 different angles

Answer 6

@amistre64 I didn't know that... Sorry!!! and thanks too !

Answer 7

1)
tan^-1(tan(3pi/4)
tan^-1(-1) = -pi/4

Answer 8

2) cos^-1 ( cos (7pi /6))
= cos^-1 ( cos (pi + pi/6))
= cos^-1 ( - cos (pi/6))
= cos^-1 ( - sqrt(3)/2)
= 5pi/6

Now try rest similarly

Answer 9

Just remember
See the attachement