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3 years ago

7

During the first half of a game you scored eight points in the second half you may only three point baskets you finish the game

with 23 points right and solve an equation to find out how many three-point basket you made

1 answer:

Mashutka [201]3 years ago

4 0

It will be 7:23 because you divid wich gives you 7

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Find all solutions of each equation on the interval 0 ≤ x < 2π.

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How are tangents and secants related to sines and cosines?

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$\displaystyle \sec{x} = \frac{1}{\cos{x}}$ .

Sticking to either cosine or sine might help simplify the calculation. By the Pythagorean Theorem, $\sin^{2}{x} = 1 - \cos^{2}{x}$ . Therefore, for the square of tangents,

$\displaystyle \tan^{2}{x} = \frac{\sin^{2}{x}}{\cos^{2}{x}} = \frac{1 - \cos^{2}{x}}{\cos^{2}{x}}$ .

This equation will thus become:

$\displaystyle \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} \cdot \frac{1}{\cos^{2}{x}} + \frac{2}{\cos^{2}{x}} - \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} = 2$ .

To simplify the calculations, replace all $\cos^{2}{x}$ with another variable. For example, let $u = \cos^{2}{x}$ . Keep in mind that $0 \le \cos^{2}{x} \le 1 \implies 0 \le u \le 1$ .

$\displaystyle \frac{1 - u}{u^{2}} + \frac{2}{u} - \frac{1 - u}{u} = 2$ .

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Solve this equation for $u$ :

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$u^{2} = 1$ .

Given that $0 \le u \le 1$ , $u = 1$ is the only possible solution.

$\cos^{2}{x} = 1$ ,

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Given that $0 \le x < 2\pi$ ,

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$k = 0$ or $k = 1$ . Accordingly,

$x = 0$ or $x = \pi$ .

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