Chapter 5: Q. 27 (page 464)

Write $\sin (2 \cos^{- 1} x)$ as an algebraic function.

Short Answer

Expert verified

The given expression as an algebraic function is $2 x (\sqrt{1 - x^{2}}) .$

Step by step solution

Step 1. Given Information.

The given trigonometric expression is $\sin (2 \cos^{- 1} x) .$

Step 2. Write the given expression as an algebraic function.

To write the given expression as an algebraic function, let $θ = \cos^{- 1} x .$

As we know, $\cos = \frac{b}{h},$ here role="math" $b = x and h = 1 .$

By using Pythagoras theorem,

$h^{2} = b^{2} + p^{2} 1^{2} = x^{2} + p^{2} \sqrt{1 - x^{2}} = p$

Now,

$\sin (2 θ) = 2 \sin θ \cos θ = 2 (\frac{\sqrt{1 - x^{2}}}{1}) (\frac{x}{1}) = 2 x (\sqrt{1 - x^{2}})$

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Write $\sin (2 \cos^{- 1} x)$ as an algebraic function.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Write the given expression as an algebraic function.

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Write sin(2cos-1x)as an algebraic function.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Write the given expression as an algebraic function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Write $\sin (2 \cos^{- 1} x)$ as an algebraic function.