Reciprocal trig functions

Question 1

How do you draw the graph y=Sin -1 (x) (y=arcsinx) graph?

Answer 1

1) draw sin graph
2) restrict at -π/2 ≤ x ≤ π/2
3) reflect in line y=x
4) swap x and y coordinates eg (π/2 , 1) becomes (1, π/2)

Question 2

Where do you restrict the domain for the arcsinx graph?

Answer 2

-π/2 ≤ x ≤ π/2

Question 3

How do you draw the y=Cos -1 (x) (y=arccosx) graph?

Answer 3

1) draw cos graph
2) restrict at 0 ≤ x ≤ π
3) reflect in line y=x
4) swap x and y coords eg (π , -1) becomes (-1, π)

Question 4

Where do you restrict the domain for the arccos graph?

Answer 4

0 ≤ x ≤ π

Question 5

How do you draw the y=Tan -1 (x) (y=arctanx) graph?

Answer 5

1) draw tan graph
2) restrict at -π/2 ≤ x ≤ π/2
2) reflect
4) asymptotes become horizontal

Question 6

Where do you restrict the domain for the arctan graph?

Answer 6

restrict at -π/2 ≤ x ≤ π/2
draw asymptotes here