Chapter 6: Q.48 (page 395)

Find the exact value of each of the remaining trigonometric functions of $θ$
$\cos θ = \frac{4}{5}, 270^{o} < θ < 360^{o}$

Short Answer

Expert verified

The exact 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

$\cos θ = \frac{4}{5}, 270^{0} < θ < 360^{0}$ is given.

We have to find the exact value of each of the remaining trigonometric functions.

Step 2. Find the value of sinθ

$W e k n o w t h a t \sin^{2} θ + \cos^{2} θ = 1, h e r e \cos θ = \frac{4}{5} \sin θ = \pm \sqrt{1 - \cos^{2} θ}, h e r e θ l i e s o n 270^{o} < θ < 360^{o} s o \cos θ i s o n f o u r t h q u a d r a n t a l l o t h e r e x c e p t \cos θ a n d s e c θ a r e w i l l b e n e g a t i v e . h e n c e \sin θ = - \sqrt{1 - c o s^{2} θ} = - \sqrt{1 - \frac{4^{2}}{5^{2}}} = - \sqrt{1 - \frac{16}{25}} = - \frac{3}{5}$

step 3. Find the values of secθ, 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. Find the values of tanθ and cotθ

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

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Find the exact value of each of the remaining trigonometric functions of $θ$
$\cos θ = \frac{4}{5}, 270^{o} < θ < 360^{o}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the value of sinθ

step 3. Find the values of secθ, cscθ

Step 4. Find the values of tanθ and cotθ

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Find the exact value of each of the remaining trigonometric functions of θcosθ=45,270o<θ<360o

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the value of sinθ

step 3. Find the values of secθ, cscθ

Step 4. Find the values of tanθ and cotθ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $θ$
$\cos θ = \frac{4}{5}, 270^{o} < θ < 360^{o}$