Draw the graph of y = sin⁻¹ x. Mark the points for x = −1, −1/2, 0, 1/2 and 1, and write its domain and range.

1. 1 · Write what is given and what is to be found. To draw: y = sin⁻¹ x with five marked points. To write: its domain and range.
2. 2 · Write the rule. y = sin⁻¹ x is the mirror image of y = sin x on [−π/2, π/2] in the line y = x.
3. 3 · Find the points.
   • sin⁻¹(−1) = −π/2, sin⁻¹(−1/2) = −π/6, sin⁻¹ 0 = 0
   • sin⁻¹(1/2) = π/6, sin⁻¹ 1 = π/2
   • Points: (−1, −π/2), (−1/2, −π/6), (0, 0), (1/2, π/6), (1, π/2)
4. 4 · Draw the figure or sketch. Draw and label both axes. Mark −1 and 1 on the x-axis and −π/2 and π/2 on the y-axis. Plot the five points and join them with a smooth increasing curve that is steep near the ends. Put solid dots at (−1, −π/2) and (1, π/2), and label the curve y = sin⁻¹ x.
5. 5 · Check and box the answer. Domain [−1, 1], range [−π/2, π/2]. The curve rises from left to right and stops at x = ±1.

Scoring tip: Label the curve, the axes and every plotted point. A neat labelled sketch is what earns the graph marks.