Soit a une mesure d'un angle orienté. Recopie et exprime chacune des expressions suivantes en fonction de tan…

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Soit a une mesure d'un angle orienté. Recopie et exprime chacune des expressions suivantes en fonction de tan a.

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Here are the expressions in terms of tan α: a) Step 1: Use the property that tan(−x) = −tan(x). tan(−α) = −tan(α) The expression is −tan(α). b) Step 1: Use the property that tan(π − x) = −tan(x). tan(π − α) = −tan(α) The expression is −tan(α). c) Step 1: Use the property that tan((π)/(2) − x) = cot(x). Step 2: Express cot(x) in terms of tan(x). tan((π)/(2) − α) = cot(α) = (1)/(tan(α)) The expression is (1)/(tan(α)). d) Step 1: Use the property that tan(π + x) = tan(x). tan(π + α) = tan(α) The expression is tan(α). e) Step 1: Use the property that tan((π)/(2) + x) = −cot(x). Step 2: Express cot(x) in terms of tan(x). tan((π)/(2) + α) = −cot(α) = −(1)/(tan(α)) The expression is −(1)/(tan(α)).

Soit a une mesure d'un angle orienté. Recopie et exprime chacune des expressions suivantes en fonction de tan a.

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Step-by-step solution

Part a· 1 step

Use the property that $\tan(-x) = -\tan(x)$ .

Part b· 1 step
$-\tan(\alpha)$

Use the property that $\tan(\pi - x) = -\tan(x)$ .

Part c· 2 steps
$\frac{1}{\tan(\alpha)}$

Use the property that $\tan(\frac{\pi}{2} - x) = \cot(x)$ .

Express $\cot(x)$ in terms of $\tan(x)$ .

Part d· 1 step
$\tan(\alpha)$

Use the property that $\tan(\pi + x) = \tan(x)$ .

Part e· 2 steps
$-\frac{1}{\tan(\alpha)}$

Use the property that $\tan(\frac{\pi}{2} + x) = -\cot(x)$ .

Express $\cot(x)$ in terms of $\tan(x)$ .

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Soit a une mesure d'un angle orienté. Recopie et exprime chacune des expressions suivantes en fonction de tan a.

Answers

Step-by-step solution

Part a· 1 step

Use the property that tan⁡(−x)=−tan⁡(x)\tan(-x) = -\tan(x)tan(−x)=−tan(x).

Part b· 1 step−tan⁡(α)-\tan(\alpha)−tan(α)

Use the property that tan⁡(π−x)=−tan⁡(x)\tan(\pi - x) = -\tan(x)tan(π−x)=−tan(x).

Part c· 2 steps1tan⁡(α)\frac{1}{\tan(\alpha)}tan(α)1​

Use the property that tan⁡(π2−x)=cot⁡(x)\tan(\frac{\pi}{2} - x) = \cot(x)tan(2π​−x)=cot(x).

Express cot⁡(x)\cot(x)cot(x) in terms of tan⁡(x)\tan(x)tan(x).

Part d· 1 steptan⁡(α)\tan(\alpha)tan(α)

Use the property that tan⁡(π+x)=tan⁡(x)\tan(\pi + x) = \tan(x)tan(π+x)=tan(x).

Part e· 2 steps−1tan⁡(α)-\frac{1}{\tan(\alpha)}−tan(α)1​

Use the property that tan⁡(π2+x)=−cot⁡(x)\tan(\frac{\pi}{2} + x) = -\cot(x)tan(2π​+x)=−cot(x).

Express cot⁡(x)\cot(x)cot(x) in terms of tan⁡(x)\tan(x)tan(x).

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Use the property that $\tan(-x) = -\tan(x)$ .

Part b· 1 step
$-\tan(\alpha)$

Use the property that $\tan(\pi - x) = -\tan(x)$ .

Part c· 2 steps
$\frac{1}{\tan(\alpha)}$

Use the property that $\tan(\frac{\pi}{2} - x) = \cot(x)$ .

Express $\cot(x)$ in terms of $\tan(x)$ .

Part d· 1 step
$\tan(\alpha)$

Use the property that $\tan(\pi + x) = \tan(x)$ .

Part e· 2 steps
$-\frac{1}{\tan(\alpha)}$

Use the property that $\tan(\frac{\pi}{2} + x) = -\cot(x)$ .

Express $\cot(x)$ in terms of $\tan(x)$ .