Chapter 6: Q.45 (page 395)

Find the exact value of each of the remaining trigonometric functions of $θ$
$\cos θ = \frac{- 4}{5} i n 3 r d q u a d r a n t$

Short Answer

Expert verified

the values are $\sin θ = - \frac{3}{5}, s e c θ = - \frac{5}{4}, c s c θ = - \frac{5}{3}, \tan θ = \frac{3}{4}, c o t θ = \frac{4}{3}$

Step by step solution

Step 1. Given information

Here $\cos θ = \frac{- 4}{5}, w h e r e θ l i e s o n t h i r d q a u d r a n t i s g i v e n$

we have to find exact value of each of the remaining trigonometric functions

Step 2.Description of finding the value of sinθ

$\cos θ = - \frac{4}{5} W e k n o w t h a t \sin^{2} θ + \cos^{2} θ = 1 \sin θ = \pm \sqrt{1 - \cos^{2} θ} a n d \sin c e \cos θ i s o n t h i r d q u a d r a n t a l l o t h e r e x c e p t \tan θ a n d c o t θ a r e w i l l b e n e g a t i v e . h e n c e \sin θ = - \sqrt{1 - \cos^{2} θ} = - \sqrt{1 - \frac{{(- 4)}^{2}}{5^{2}}} = - \sqrt{1 - \frac{16}{25}} = - \frac{3}{5}$

Step 3. Finding the values of secθ and cscθ

According to the question $\cos θ = - \frac{4}{5}, t h e n s e c θ = \frac{1}{\cos θ} = \frac{1}{- \frac{4}{5}} = - \frac{5}{4} c s c θ = \frac{1}{\sin θ} = \frac{1}{- \frac{3}{5}} = - \frac{5}{3}$

Step 4. Finding the value of tanθ and cotθ

since

$\sin θ = - \frac{3}{5} a n d \cos θ = - \frac{4}{5} \tan θ = \frac{\sin θ}{\cos θ} = \frac{- \frac{3}{5}}{- \frac{4}{5}} = \frac{3}{4} c o t θ = \frac{1}{\tan θ} = \frac{1}{\frac{3}{4}} = \frac{4}{3}$

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Find the exact value of each of the remaining trigonometric functions of $θ$
$\cos θ = \frac{- 4}{5} i n 3 r d q u a d r a n t$

Short Answer

Step by step solution

Step 1. Given information

Step 2.Description of finding the value of sinθ

Step 3. Finding the values of secθ and cscθ

Step 4. Finding the value of tanθ and cotθ

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Step by step solution

Step 1. Given information

Step 2.Description of finding the value of sinθ

Step 3. Finding the values of secθ and cscθ

Step 4. Finding the value of tanθ and cotθ

One App. One Place for Learning.

Most popular questions from this chapter

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Find the exact value of each of the remaining trigonometric functions of $θ$
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