Question

Match each expression on the left with one on the right that completes each equation as an identity. A. 1 B. $-\tan ^{2} x$ C. $\cot ^{2} x$ D. $\sin x$ E. $-\sin ^{2} x$ F.$$\frac{1}{\sin x \cos x}$$ G. $1+\cot ^{2} x$ H. $\cos ^{2} x$ I. $\csc x$ J. $1+\cot x$ $$\frac{\csc x}{\sin x}=?$$

Name: Problem 9, Chapter 6: Precalculus Functions and Graphs
Uploaded: 2020-03-29T13:42:30-08:00
Duration: 1 min 8 s
Channel: Tony Ni
Description: Match each expression on the left with one on the right that completes each equation as an identity. A. 1 B. -tan^2 x C. cot^2 x D. sinx E. -sin^2 x F.(1)/(sinx cosx) G. 1+cot^2 x H. cos^2 x I. cscx J. 1+cotx (cscx)/(sinx)=?

   Match each expression on the left with one on the right that completes each equation as an identity.
A. 1
B. $-\tan ^{2} x$
C. $\cot ^{2} x$
D. $\sin x$
E. $-\sin ^{2} x$
F.$$\frac{1}{\sin x \cos x}$$
G. $1+\cot ^{2} x$
H. $\cos ^{2} x$
I. $\csc x$
J. $1+\cot x$
$$\frac{\csc x}{\sin x}=?$$

Precalculus Functions and Graphs

Mark Dugopolski 4th Edition

Chapter 6, Problem 9

Instant Answer

Solved by Expert Tony Ni

03/29/2020

Step 1

We know that $\csc x$ is the reciprocal of $\sin x$, so we can rewrite the expression as $\frac{1}{\sin x} \cdot \frac{1}{\sin x}$. Show more…

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Match each expression on the left with one on the right that completes each equation as an identity. A. 1 B. $-\tan ^{2} x$ C. $\cot ^{2} x$ D. $\sin x$ E. $-\sin ^{2} x$ F.$$\frac{1}{\sin x \cos x}$$ G. $1+\cot ^{2} x$ H. $\cos ^{2} x$ I. $\csc x$ J. $1+\cot x$ $$\frac{\csc x}{\sin x}=?$$

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Key Concepts

Trigonometric Function Definitions

This concept involves understanding the basic definitions of trigonometric functions. For example, tangent is defined as the ratio of sine to cosine. Knowing these definitions allows one to express trigonometric functions in terms of one another, which is essential for manipulating and simplifying expressions.

Quotient Identity

The quotient identity states that tan x equals sin x divided by cos x. This identity is key in converting expressions involving tangent and cosine into a form where common factors may cancel, thereby simplifying the expression.

Algebraic Simplification in Trigonometry

Algebraic simplification involves substituting known trigonometric identities and canceling common factors. In this context, multiplying cosine by the quotient sin x/cos x allows for the cancellation of cosine, which simplifies the expression to sin x.

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