Chapter 6: Q. 58 (page 396)

Find the exact value of each of the remaining trigonometric functions of $θ .$
$secθ = - 2, tanθ > 0$

Short Answer

Expert verified

The exact values of trigonometric functions are,

$sinθ = - \frac{\sqrt{3}}{2} tanθ = \sqrt{3} cotθ = \frac{\sqrt{3}}{3} cscθ = - \frac{2 \sqrt{3}}{3}$

Step by step solution

Step 1. Given Information

Given that the trigonometric function is $secθ = - 2, tanθ > 0 .$ To find the exact values of trigonometric function using substitution.

Step 2. Solving a equation

It implies that $sinθ < 0$ in III quadrant. On using the equation,

$\sin^{2} θ + \cos^{2} θ = 1 sinθ = \pm \sqrt{1 - \cos^{2} θ}$

On substituting the value of $cosθ = - \frac{1}{2}$ in the equation,

$sinθ = - \sqrt{1 - {(- \frac{1}{2})}^{2}} = - \sqrt{1 - \frac{1}{4}} sinθ = - \frac{\sqrt{3}}{2}$

Step 3. Substitution

On substituting the value in equation,

$tanθ = \frac{y}{x} = \frac{sinθ}{cosθ} = \frac{- \frac{\sqrt{3}}{2}}{- \frac{1}{2}} tanθ = \sqrt{3} cotθ = \frac{1}{tanθ} cotθ = \frac{\sqrt{3}}{3} cscθ = \frac{1}{sinθ} = \frac{1}{- \frac{\sqrt{3}}{2}} cscθ = - \frac{2 \sqrt{3}}{3}$

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Find the exact value of each of the remaining trigonometric functions of $θ .$
$secθ = - 2, tanθ > 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solving a equation

Step 3. Substitution

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Find the exact value of each of the remaining trigonometric functions of θ.secθ=-2,tanθ>0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solving a equation

Step 3. Substitution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Geometry

Decision Maths

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $θ .$
$secθ = - 2, tanθ > 0$