Roots of Cubic Equations and Trigonometry 2

$$2\cos A\sin B$$

$$-2\sin A\cos B$$

2cosAcosB

-2sinAsinB

$$5\cos\left(\theta+\alpha\right)$$ where $$\tan\alpha=\frac{3}{4}$$

$$5\sin\left(\theta-\alpha\right)$$ where $$\tan\alpha=\frac{3}{4}$$

$$5\cos\left(\theta+\alpha\right)$$ where $$\tan\alpha=\frac{4}{3}$$

$$5\cos\left(\theta-\alpha\right)$$ where $$\tan\alpha=\frac{4}{3}$$

for $$-\frac{\pi}{2}<\theta<\frac{\pi}{2}$$ , $$f\left(\theta\right)>0$$

$$f\left(\theta\right)$$ is periodic with a period of $$\pi$$

$$f\left(\theta\right)$$ is undefined when $$\theta=\left(2n+1\right)\ \frac{\pi}{2}$$

$$-1<f\left(\theta\right)<1$$

$$\theta$$ lies in quadrants 1 and 2

the principal solution is $$\theta=\frac{\pi}{4}$$

$$\cos\theta=\sqrt[]{2}$$

the general solution is $$\theta=n\pi\pm\frac{\pi}{4}$$

3

1

$$\sqrt[]{41}$$

$$\pm5$$

$$\pm\sqrt[]{41}$$

$$\theta=2n\pi\pm\frac{\pi}{6}$$

$$\theta=n\pi+\frac{\pi}{3}$$

$$\theta=2n\pi+\frac{\pi}{3}$$

$$\theta=2n\pi\pm\frac{\pi}{3}$$

$$\theta=n\pi\pm\frac{\pi}{6}$$

-0.2

0.5

1.9

2.6

$$x^3-2x^2-5x-6=0$$

$$x^3-2x^2-5x+6=0$$

$$x^3-2x^2+5x+6=0$$

$$x^3+2x^2+5x+6=0$$

$$x^3-8x^2-48x-256=0$$

$$x^3-8x^2+48x-256=0$$

$$4x^3-8x^2+12x+16=0$$

$$4x^3-8x^2+12x-16=0$$