TI - Solve Equations Using Basic Identities Lesson

Solving Equations using Basic Identities

Recall, in the first module we learned about some trigonometric identities: quotient, reciprocal and Pythagorean.

Try these problems to review those:

Watch this video to recall how to verify identities:

On a separate sheet of paper, verify the identities below:

1. equation image indicator $LaTeX: \left(\cos^2\theta-1\right)\left(\tan^2\theta+1\right)=-\tan^2\theta$ $\left(\cos^2\theta-1\right)\left(\tan^2\theta+1\right)=-\tan^2\theta$

2. equation image indicator $LaTeX: \frac{\tan^2\theta+1}{\tan^2\theta}=\csc^2\theta$ $\frac{\tan^2\theta+1}{\tan^2\theta}=\csc^2\theta$

3. equation image indicator $LaTeX: \tan B+\cot B=\csc B\sec B$ $\tan B+\cot B=\csc B\sec B$

In a previous chapter, we learned how to solve trigonometric equations. Let's look at a problem that we've already done:

Find all solutions for the equation equation image indicator $LaTeX: 4\sin^2x+1=4$ $4\sin^2x+1=4$ , over the interval $LaTeX: \left[0,\:2\pi\right)$ $\left[0,\:2\pi\right)$ .

equation image indicator $LaTeX: 4\sin^2x+1=4\\ 4\sin^2x=3\\ \sin^2x=\frac{3}{4}\\ \sin x=\pm\sqrt[]{\frac{3}{4}}\\ \sin x=\pm\frac{\sqrt[]{3}}{2} \\ x=\frac{\pi}{3},\:\frac{2\pi}{3},\:\frac{4\pi}{3},\:\frac{5\pi}{3}$ $4\sin^2x+1=4\\ 4\sin^2x=3\\ \sin^2x=\frac{3}{4}\\ \sin x=\pm\sqrt[]{\frac{3}{4}}\\ \sin x=\pm\frac{\sqrt[]{3}}{2} \\ x=\frac{\pi}{3},\:\frac{2\pi}{3},\:\frac{4\pi}{3},\:\frac{5\pi}{3}$

Now, watch these videos to try a type of problem you haven't seen before:

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