Chapter 6: Q. 21 (page 437)

find the value of the remaining five trigonometric functions of
$\tan ϑ = \frac{- 12}{5} π / 2 < ϑ < π$

Short Answer

Expert verified

the value of the remaining five trigonometric functions of $ϑ$ are:

$\cos ϑ = - \frac{5}{13} \sin ϑ = \frac{12}{13} \cos e c ϑ = \frac{13}{12} s e c ϑ = - \frac{13}{5} c o t ϑ = - \frac{5}{12}$

Step by step solution

Step 1. Given information

$\tan ϑ = \frac{- 12}{5} π / 2 < ϑ < π$

Step 2. Solving for secϑ & cosϑ

We know that ;

$\tan^{2} ϑ + 1 = s e c^{2} ϑ$

Using this equation:

$s e c ϑ = \sqrt{1 + \tan^{2} ϑ} s e c ϑ = \sqrt{1 + {(- \frac{12}{5})}^{2}} s e c ϑ = \sqrt{1 + \frac{144}{25}} s e c ϑ = \sqrt{\frac{169}{25}} s e c ϑ = \frac{13}{5}$

Since theta is in second quadrant so;

$s e c ϑ = - \frac{13}{5}$

Step 3. Solving forcosϑ , sinϑ , cotϑ ,cosecϑ

We know that :

$\cos e c ϑ = \frac{1}{\sin ϑ} s e c ϑ = \frac{1}{\cos ϑ} c o t ϑ = \frac{1}{\tan ϑ}$

Using this :

$\cos ϑ \frac{- 5}{13} \sin ϑ = \cos ϑ \times \tan ϑ \sin ϑ = \frac{12}{13} c o t ϑ = \frac{- 5}{12} \cos e c ϑ = \frac{13}{12}$

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find the value of the remaining five trigonometric functions of
$\tan ϑ = \frac{- 12}{5} π / 2 < ϑ < π$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving for secϑ & cosϑ

Step 3. Solving forcosϑ , sinϑ , cotϑ ,cosecϑ

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find the value of the remaining five trigonometric functions of tanϑ=-125π/2<ϑ<π

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving for secϑ & cosϑ

Step 3. Solving forcosϑ , sinϑ , cotϑ ,cosecϑ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

find the value of the remaining five trigonometric functions of
$\tan ϑ = \frac{- 12}{5} π / 2 < ϑ < π$