How do I compute these plot points?

Question

Consider the function q(x, y) = sin^-1(x + y − 2) + cos^-1(2x + 3y − 6).

Compute the following values, if possible:

a. q( 3, 0)

b. q( 0, 0)

c. q(−1/2, 2)

d. q( 1, 3/2)

e. q( 3, −1/2)

f. Sketch the domain of q( x, y) on paper.

Answer 1

q(x, y) = sin^-1(x + y − 2) + cos^-1(2x + 3y − 6)

a. sin^-1(1) + cos^-1(0) = π/2 + π/2 = π

b. sin^-1(-2) + cos^-1(-6) DNE

c. sin^-1(-1/2) + cos^-1(-1) = -π/6 + π = 5π/6

d. sin^-1(1/2) + cos^-1(1/2) = π/6 + π/3 = π/2

e. sin^-1(1/2) + cos^-1(-3/2) DNE

f. You have to graph intersection of set of solutions of system of inequalities:

Ix + y − 2I ≤ 1 and I2x + 3y - 6I ≤ 1.

I don't know how to do graphs in this editor

Answer 2

desmos.com/calculator/6lxtbi9hhr