Chapter 6: Q. 19 (page 437)

find the value of the remaining five trigonometric functions of $ϑ$
$\sin ϑ = \frac{5}{7}$ , $ϑ$ in Second Quadrant.

Short Answer

Expert verified

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

$\cos ϑ = - \frac{2 \sqrt{6}}{7} \tan ϑ = - \frac{5}{2 \sqrt{6}} \cos e c ϑ = \frac{7}{5} s e c ϑ = - \frac{7}{2 \sqrt{6}} c o t ϑ = - \frac{2 \sqrt{6}}{5}$

Step by step solution

Step 1. Given information

$\sin ϑ = \frac{5}{7}$ , $ϑ$ in Second Quadrant.

Step 2. Solving for cosϑ

We know ;

$\sin^{2} ϑ + \cos^{2} ϑ = 1$

Using this equation :

$\cos ϑ = \sqrt{1 - \sin^{2} ϑ} \cos ϑ = \sqrt{1 - {(\frac{5}{7})}^{2}} \cos ϑ = \sqrt{1 - \frac{25}{49}} \cos ϑ = \sqrt{\frac{24}{49}} \cos ϑ = \frac{2 \sqrt{6}}{7}$

Since theta is in second quadrant so,

$\cos ϑ = - \frac{2 \sqrt{6}}{7}$

Step 3. Solving forcotϑ , secϑ , cosecϑ

We know ;

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

Using the above identities :

$\tan ϑ = - \frac{5}{2 \sqrt{6}} \cos e c ϑ = \frac{7}{5} s e c ϑ = - \frac{7}{2 \sqrt{6}} c o t ϑ = - \frac{2 \sqrt{6}}{5}$

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find the value of the remaining five trigonometric functions of $ϑ$
$\sin ϑ = \frac{5}{7}$ , $ϑ$ in Second Quadrant.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving for cosϑ

Step 3. Solving forcotϑ , secϑ , cosecϑ

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find the value of the remaining five trigonometric functions of ϑsinϑ=57, ϑ in Second Quadrant.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving for cosϑ

Step 3. Solving forcotϑ , secϑ , cosecϑ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Pure Maths

Probability and Statistics

Geometry

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

find the value of the remaining five trigonometric functions of $ϑ$
$\sin ϑ = \frac{5}{7}$ , $ϑ$ in Second Quadrant.