/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 35 Verify each identity. $$\cos \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 35

Verify each identity. $$\cos \left(x-\frac{\pi}{2}\right)=\sin x$$

Short Answer

Expert verified
Verified that \(\cos \left(x-\frac{\pi}{2}\right)=\sin x\) is indeed a valid identity.

Step by step solution

01

Analyze the left side of the given identity

Given the identity \(\cos \left(x-\frac{\pi}{2}\right)=\sin x\), start by focusing on the left side of the equation. This expression involves a cosine function, specifically \(\cos\) of some quantity.
02

Use the co-function identity

The co-function identity can be applied here. According to this identity, for all values of x in the domain, \(\cos\left(\frac{\pi}{2} - x\right) = \sin(x)\). It's important to note that the subtraction of two angles equals the negative of the subtraction in reverse order, meaning \( cos\left(x - \frac{\pi}{2}\right) = cos\left(-\left(\frac{\pi}{2} - x\right)\right)\).
03

Apply the co-function identity

Now apply the co-function identity to the expression on the left side, substituting \(\cos\left(x - \frac{\pi}{2}\right)\) with \(\sin\left(\frac{\pi}{2} - x\right)\).
04

Simplifying the expression

Since any number subtracted from itself results in zero, \(\sin\left(\frac{\pi}{2} - x\right)\) simplifies to \(\sin x\).
05

Verify the identity

Finally, check to see whether the transformed left side is the same as the right side. As the transformed left side is \(\sin x\) and the right side is also \(\sin x\), this verifies that the given trigonometric identity holds true.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve each equation on the interval \([0,2 \pi)\) \(2 \cos ^{3} x+\cos ^{2} x-2 \cos x-1=0\) (Hint: Use factoring by grouping.)

Solve each equation on the interval \([0,2 \pi)\) $$3 \cos ^{2} x-\sin x=\cos ^{2} x$$

Find the exact value of each expression. Do not use a calculator. $$\cos \left[\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)-\sin ^{-1}\left(-\frac{1}{2}\right)\right]$$

Use this information to solve. A ball on a spring is pulled 4 inches below its rest position and then released. After t seconds, the balls distance, \(d\), in inches from its rest position is given by $$d=-4 \cos \frac{\pi}{3} t$$ Find all values of \(t\) for which the ball is 2 inches below its rest position.

Use a graphing utility to approximate the solutions of each equation in the interval \([0,2 \pi) .\) Round to the nearest hundredth of a radian. $$\sin 2 x=2-x^{2}$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.