Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

When two railroad tracks merge, the overlapping portions of the tracks are in the shapes of circular arcs (see figure). The radius of each arc $ r $ (in feet) and the angle $ \theta $ are related by

$ \dfrac{x}{2} = 2r \sin^2 \dfrac{\theta}{2} $

Write a formula for $ x $ in terms of $ \cos \theta $.

$x=2 r-2 r \cos \theta$

00:58

Amy J.

Precalculus

Algebra

Chapter 5

Analytic Trigonometry

Section 5

Multiple-Angle and Product-to-Sum Formulas

Trigonometry

Introduction to Trigonometry

Baylor University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

00:59

When two railroad tracks m…

02:03

Railroad Curves In the Uni…

0:00

RAILROAD TRACK DESIGN The …

08:41

Railroad Track Design The …

01:19

Railroad tracks follow a…

01:52

At their point of intersec…

01:03

A central angle $\theta$ i…

02:35

Find all the points of int…

02:20

Find all points at which t…

The figure shows a highway…

So we're given this formula X over to is equal to two are sine squared of theta over two and we want to change that. So X is a function of a co sign. So we wanna have X and co sign in the function, which means we don't want this angle here, and it didn't even say and co sign of data we just wanted co sign. So we have to get rid of the sine squared. So we have an identity that says that if you have the sine squared oven angle, they give a formula in terms of you that that that's equivalent to one minus the co sign off to you all over to. And this comes from actually the the double angle formula for co sign and doing a little bit of substituting. So this is the identity that we want to use. So let's do it. So we have I will do a little substitution. We have X over to which will multiply both sides by two in a minute, is equal to to our times. And now we needed to do a substitution for sine squared. And so we're gonna have one minus and you is acting as data over to So I have one minus cosine off. And then I need to take two times you and this whole thing is acting as you. So I have data over to and nicely enough we can see what's going to end up happening there, that these twos, they're going to cancel and lo and behold, these twos they're going to cancel. And then if I multiply both sides by two, will have X is equal to, and I have a two are here. So this combines together to be to our and I'm going to distribute it. So I have to our times one minus to our times the co signed of data and there is our function written in terms of cosign, and that's a simpler function to plug things into, then is this function and we're all done

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, the absolute value or modulus |x| of a real number x is its …

When two railroad tracks merge, the overlapping portions of the tracks are i…

Railroad Curves In the United States, circular railroad curves are designate…

RAILROAD TRACK DESIGN The circular arc of a railroad curve has a chord of le…

Railroad Track Design The circular arc of a railroad curve has a chord of le…

Railroad tracks follow a circular curve of radius 500.0 $\mathrm{m}$ and a…

At their point of intersection, the angle $\theta$ between any two nonparall…

A central angle $\theta$ in a circle of radius $r$ intercepts a chord of len…

Find all the points of intersection of the given curves.

$ r^2 = \si…

Find all points at which the two curves intersect.$r=1-2 \sin \theta$ an…

The figure shows a highway sign that warns of a railway crossing. The lines …

02:07

In Exercises 11 - 20, solve the system by the method of substitutio…

01:02

In Exercises 81-90, use the product-to-sum formulas to write the product as …

03:21

In Exercises 53-58, determine whether $\mathbf{u}$ and $\mathbf{v}$ are orth…

01:50

In Exercises 13 - 30, solve the system by the method of elimination…

02:46

In Exercises 35 - 48, solve the system graphically.

$ \left\{\…

05:56

Exercises 43-52, use the power-reducing formulas to rewrite the expression i…

00:56

In Exercises 111 - 124, verify the identity.

$ 1 + \cos 10y = 2…

02:21

In Exercises 107 and 108, use the figure, which shows two lines …

06:12

BRAKING LOAD A truck with a gross weight of 30,000 pounds is parked on a slo…

00:13

Fill in the blanks.

A ________ of a system of equations is…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.