Area Between Two Curves (Sin and Cos)

[Jet1045]

Homework Statement

Sketch the regions enclosed by the given curves. And determine the area between the curves.
y = 7 cos 3x, y = 7 sin 6x, x = 0, x = π/6

Homework Equations

The Attempt at a Solution

Okay so i ended up solving the question, because i used the help of my graphing calculator. To get the area between the two curves you need the intersection point between the two curves so that you can determine the limits of integration for the two integrals. However, i have no idea how you solve for the intersection point of those two trigonometric functions by hand. Maybe its really easy, and i am just having a dumb moment, but i needed to use my calculator to get it and of course you can't use calculators in university calc classes (or at least in mine). Someone pleaseee explain how to do this by hand if you can :)

 

[SammyS]

Homework Statement

Sketch the regions enclosed by the given curves. And determine the area between the curves.
y = 7 cos 3x, y = 7 sin 6x, x = 0, x = π/6
...

The Attempt at a Solution

Okay so i ended up solving the question, because i used the help of my graphing calculator. To get the area between the two curves you need the intersection point between the two curves so that you can determine the limits of integration for the two integrals. However, i have no idea how you solve for the intersection point of those two trigonometric functions by hand. Maybe its really easy, and i am just having a dumb moment, but i needed to use my calculator to get it and of course you can't use calculators in university calc classes (or at least in mine). Someone pleaseee explain how to do this by hand if you can :)

(My spell checker said that you spelled 'please' incorrectly.)
Can you give the equation you would use to solve for the point of intersection?

 

[Curious3141]

Homework Statement

Sketch the regions enclosed by the given curves. And determine the area between the curves.
y = 7 cos 3x, y = 7 sin 6x, x = 0, x = π/6

Homework Equations

The Attempt at a Solution

Okay so i ended up solving the question, because i used the help of my graphing calculator. To get the area between the two curves you need the intersection point between the two curves so that you can determine the limits of integration for the two integrals. However, i have no idea how you solve for the intersection point of those two trigonometric functions by hand. Maybe its really easy, and i am just having a dumb moment, but i needed to use my calculator to get it and of course you can't use calculators in university calc classes (or at least in mine). Someone pleaseee explain how to do this by hand if you can :)

To find the intersection point, set 7cos3x = 7sin6x, or simply cos3x = sin6x, since the sevens cancel out.

Then observe that sin6x = sin(2*3x), and use the double-angle formula for sine. Can you go from here?

 

[Jet1045]

To find the intersection point, set 7cos3x = 7sin6x, or simply cos3x = sin6x, since the sevens cancel out.

Then observe that sin6x = sin(2*3x), and use the double-angle formula for sine. Can you go from here?

OHH i didnt know it would be that complicated, i thought you could just set them equal to each other and there would be something obvious that i was just missing. K i will look up the double angle formula cause i have totally forgotten that stuff from high school. Thanks though :)

 

[Curious3141]

OHH i didnt know it would be that complicated, i thought you could just set them equal to each other and there would be something obvious that i was just missing. K i will look up the double angle formula cause i have totally forgotten that stuff from high school. Thanks though :)

Let me help you out: sin2θ = 2sinθcosθ.

Now put θ=3x.

 

[iamjaskaran]

can anyone tell me how i post my problem in my account..??pleasez

 

[SammyS]

can anyone tell me how i post my problem in my account..??pleasez

Hello amjaskaran. Welcome to PF !

Use the "new topic" button in the appropriate Homework section, such as 'Calculus & Beyond', or 'Pre-Calculus', or 'Introductory Physics', etc.