graph x = 7 sin t + sin 7ty = 7 cos t + cos 7t?
How can I graph the equations ( x = 7 \sin(t) + \sin(7t) ) and ( y = 7 \cos(t) + \cos(7t) )? What steps should I follow to ensure an accurate representation of this graph?
4 Answers
Should look like that. Don't ask me why that is, though I can probably make some guesses. Notice that if you were to draw a rough circle on the midpoints of the rounded edges of the "cloud-shaped-figure," it would have a radius of 7. This is probably because of the amplitudes of the sinusoids you are adding together in each equation. If you were to only graph the 7sin(t) and the 7cos(t) parts, it would produce this circle. However, once you add the sin(7t) and the cos(7t) into the mix, it creates a sort of variable sinusoidal axis, so it becomes a sinusoid around the circle (which acts as the "varying sinusoidal axis."
I did notice that the humps on the cloud also resemble a cycloid, which you can read about here: http://mathworld.wolfram.com/Cycloid.html Anyways, that's my input, but this is a tough question that most high school teachers would not expect you to know how to do without any help.
an interesting graph...looks like a fluffy cloud made up of 8 semi-circles
Related Questions
Find the circumference of a circle with a radius of 5 inches. Please express your answer in terms of pi.
How tall is 77 inches when converted to feet?
In circle O, ST is a diameter. What is the value of x if (2x + 8) equals one of the following options: 22.0, 25.0, 25.4,...
I have a question regarding torque in a magnetism context. I understand that the equation τ = IABsin(θ) will be relevant...
Could you please help me find the cube roots of the complex number represented in polar form as 8(cos 216° + i sin 216°)...
Please find below the present and future values for different interest rates. Compounding and discounting occur annually...
A radio telescope features a parabolic surface, as illustrated below. Given that the telescope is 1 meter deep and 12 me...
What is the cube root of ( b^{27} )?
How many moles of CuO can be produced from 0.450 moles of Cu2O in the following reaction: 2Cu2O + O2 → 4CuO?
Suppose you are asked to calculate the area of a rectangle that is 2.1 cm wide and 5.6 cm long. Your calculator provides...