soln: From the equation different values of y = sin3x:

 x y=sin3x 0° 0 10°$$\frac{π}{18}$$ $$\frac{1}{2}$$(=0.5) 20°=$$\frac{π}{9}$$ $$\frac{\sqrt{3}}{2}$$(=0.87) 30°=$$\frac{π}{6}$$ 1 40°=$$\frac{2π}{9}$$ $$\frac{\sqrt{3}}{2}$$(=0.87) 50°=$$\frac{\sqrt{5π}}{18}$$ $$\frac{1}{2}$$(=0.5) 60°=$$\frac{π}{3}$$ 0
 70°=$$\frac{7π}{18}$$ -$$\frac{1}{2}$$(=-0.5) 80°=$$\frac{4π}{9}$$ -$$\frac{\sqrt{3}}{2}$$=-0.87 100°=$$\frac{5π}{9}$$ -1 110°=$$\frac{11π}{18}$$ -$$\frac{1}{2}$$=-0.50 120°=$$\frac{2π}{3}$$ 0
 150°$$\frac{5π}{6}$$ 1 180°=π 0

graph of above table:

soln; Different values of y = sin2θ

 θ y=sin2θ 0° 30°$$\frac{π}{6}$$ 60° 90°=$$\frac{π}{2}$$ 120°=$$\frac{2π}{3}$$ 150°=$$\frac{5π}{6}$$ 180°=π 0 $$\begin{pmatrix} 1 \\ 2 \\ \end{pmatrix}$$2=$$\frac{1}{4}$$(=0.25) $$\frac{\sqrt{3}}{2}$$2(=0.75) 1 $$\frac{\sqrt{3}}{2}$$2=0.75 $$\begin{pmatrix} 1 \\ 2 \\ \end{pmatrix}$$2=$$\frac{1}{4}$$=0.25 0=0

The graph o f the above table:

soln: Different values of y = cos2x

 θ y=cos2x 0 30°=$$\frac{π}{6}$$ 60°=$$\frac{π}{3}$$ 90°=$$\frac{π}{2}$$ 120°=$$\frac{2π}{3}$$ 150°=$$\frac{5π}{6}$$ 180°=π 0 $$\frac{1}{2}$$=0.5 $$\frac{-1}{2}$$=-0.5 -1 $$\begin{pmatrix} -1 \\ 2 \\ \end{pmatrix}$$=-0.5 $$\frac{1}{2}$$=0.5 1

The graph of above table:

Soln: Different values of y = cosθ - sinθ

 θ y=cosθ-sinθ 0° 30°=$$\frac{π}{6}$$ 60°=$$\frac{π}{3}$$ 90°=$$\frac{π}{2}$$ 120°=$$\frac{2π}{3}$$ 150°=$$\frac{5π}{6}$$ 180°=$$\frac{π}{2}$$ 1 $$\frac{\sqrt{3}}{2}$$-$$\frac{1}{2}$$=0.87-0.5=0.37 $$\frac{1}{2}$$-$$\frac{\sqrt{3}}{2}$$=0.5-0.87=-0.37 0-1=-1 -$$\frac{1}{2}$$-$$\frac{\sqrt{3}}{2}$$ = -0.5-0.87=-1.37 -$$\frac{\sqrt{3}}{2}$$-$$\frac{1}{2}$$=-0.87-0.5=-1.37 -1-0=1

The graph of above table:

soln: Different values of y = 2sinθ

 θ y=2sinθ 0° 30°=$$\frac{π}{6}$$ 60°=$$\frac{π}{3}$$ 90°=$$\frac{π}{2}$$ 120°=$$\frac{2π}{3}$$ 150°=$$\frac{5π}{6}$$ 180°=$$\frac{π}{2}$$ 0 1 $$\sqrt{3}$$=1.73 2 $$\sqrt{3}$$=1.73 1 0

The graph of the above table:

soln: Different values of y = tan2θ

 θ y=tan2θ 0° 30°=$$\frac{π}{6}$$ 60°=$$\frac{π}{3}$$ 90°=$$\frac{π}{2}$$ 120°=$$\frac{2π}{3}$$ 150°=$$\frac{5π}{6}$$ 180°=π 0 $$\sqrt{3}$$=1.73 -$$\sqrt{3}$$=-1.73 0 $$\sqrt{3}$$=1.73 -$$\sqrt{3}$$=-1.73 0

The graph of above table:

soln: Different values of y = tan$$\frac{3x}{2}$$

 θ y=tan$$\frac{3x}{2}$$ 0° 30°=$$\frac{π}{6}$$ 60°=$$\frac{π}{3}$$ 90°=$$\frac{π}{2}$$ 120°=$$\frac{2π}{3}$$ 150°=$$\frac{5π}{6}$$ 180°=π 0 1 ∞ -1 0 1 ∞

the grape of above table :