Consider the angle u in standard position in a unit circle, where 0 < /2

Consider the angle u in standard position in a unit circle, where 0 ≤ θ < π/2 or - π/2 < θ < 0 (use both figures).

a. Show that |AC| = |sin θ|, for -π/2 < θ < π/2.

b. Show that |sin θ| < |θ|, for -π/2 < θ < π/2.

c. Conclude that - |θ| ≤ sin θ ≤ |θ|, for -π/2 < θ < π/2.

d. Show that 0 ≤ 1 - cos θ ≤ |θ|, for -π/2 < θ < π/2.

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