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Sketch a polar curve for r equals negative sin theta?
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How do you apply w equals z plus 1over z to the circle absolute value z equals 2?
To apply the transformation ( w = z + \frac{1}{z} ) to the circle defined by ( |z| = 2 ), we can express ( z ) in polar form as ( z = 2e^{i\theta} ), where ( \theta ) ranges from ( 0 ) to ( 2\pi ). Substituting this into the equation for ( w ), we get ( w = 2e^{i\theta} + \frac{1}{2e^{i\theta}} = 2e^{i\theta} + \frac{1}{2} e^{-i\theta} ). This simplifies to ( w = 2e^{i\theta} + \frac{1}{2}(\cos \theta - i \sin \theta) ), which describes a new curve in the ( w )-plane. The resulting curve can be analyzed further to understand its geometric properties.
Write the curve x3 y3 3axy in polar form Hence find the area encircled by its loop?
To convert the curve (x^3 + y^3 = 3axy) into polar form, we use the substitutions (x = r\cos\theta) and (y = r\sin\theta). This gives us the polar equation (r^3(\cos^3\theta + \sin^3\theta) = 3ar^2\cos\theta\sin\theta), which simplifies to (r = \frac{3a\cos\theta\sin\theta}{\cos^3\theta + \sin^3\theta}). To find the area encircled by the loop, we can use the formula for the area in polar coordinates, (A = \frac{1}{2} \int_{\theta_1}^{\theta_2} r^2 d\theta). Evaluating this integral over one loop (typically from (0) to (\frac{\pi}{2}) for the symmetric shape) yields the area (A = \frac{3\pi a^2}{8}).
Can sine theta equals tan theta equals theta be equal for small angels?
Yes. (Theta in radians, and then approximately, not exactly.)
How do you figure this out Sin theta equals 0.0138 so theta equals what?
theta = arcsin(0.0138) is the principal value.
Sketch a polar curve for r equals negative sin theta?
I regret that the browser provided by answers.com is incapable of displaying even simple graphics.
How do you apply w equals z plus 1over z to the circle absolute value z equals 2?
To apply the transformation ( w = z + \frac{1}{z} ) to the circle defined by ( |z| = 2 ), we can express ( z ) in polar form as ( z = 2e^{i\theta} ), where ( \theta ) ranges from ( 0 ) to ( 2\pi ). Substituting this into the equation for ( w ), we get ( w = 2e^{i\theta} + \frac{1}{2e^{i\theta}} = 2e^{i\theta} + \frac{1}{2} e^{-i\theta} ). This simplifies to ( w = 2e^{i\theta} + \frac{1}{2}(\cos \theta - i \sin \theta) ), which describes a new curve in the ( w )-plane. The resulting curve can be analyzed further to understand its geometric properties.
Write the curve x3 y3 3axy in polar form Hence find the area encircled by its loop?
To convert the curve (x^3 + y^3 = 3axy) into polar form, we use the substitutions (x = r\cos\theta) and (y = r\sin\theta). This gives us the polar equation (r^3(\cos^3\theta + \sin^3\theta) = 3ar^2\cos\theta\sin\theta), which simplifies to (r = \frac{3a\cos\theta\sin\theta}{\cos^3\theta + \sin^3\theta}). To find the area encircled by the loop, we can use the formula for the area in polar coordinates, (A = \frac{1}{2} \int_{\theta_1}^{\theta_2} r^2 d\theta). Evaluating this integral over one loop (typically from (0) to (\frac{\pi}{2}) for the symmetric shape) yields the area (A = \frac{3\pi a^2}{8}).
How do you convert this polar equation r2 sin 2 theta equals 8 to cartesian form?
It's possible
Can sine theta equals tan theta equals theta be equal for small angels?
Yes. (Theta in radians, and then approximately, not exactly.)
How do you figure this out Sin theta equals 0.0138 so theta equals what?
theta = arcsin(0.0138) is the principal value.
X squared plus y squared equals 2y.change into polar equation?
x2+y2=2y into polar coordinates When converting Cartesian coordinates to polar coordinates, three standard converstion factors must be memorized: r2=x2+y2 r*cos(theta)=x r*sin(theta)=y From these conversions, you can easily get the above Cartesian equation into polar coordinates: r2=2rsin(theta), which reduces down (by dividing out 1 r on both sides) to: r=2sin(theta)
Tan theta plus cot theta equals 2csc2 theta?
Yes, it is.
Sec squared theta plus tan squared theta equals to 13 12 and sec raised to 4 theta minus tan raised to 4 theta equals to how much?
It also equals 13 12.
Sin theta equals zero answer in radians in terms of pi?
Theta equals 0 or pi.
What is cosine 2 theta when sine theta equals .28?
If sine theta is 0.28, then theta is 16.26 degrees. Cosine 2 theta, then, is 0.8432
What are other possible coordinates of a point that has the coordinates of (24)?
Another way to classify a point is with the polar system. A polar coordinate, instead of (x, y), is (r, theta). To find r, you can use the Pythagorean Theorem, a^2 + b^2 = c^2.In this case, a = 2 and b = 4, or vice versa. That means that c, or r, equals 2 square roots of 5, or 2sqrt5.To find theta, you can use this formula: theta = tan inverse(y/x). With point (2,4), theta equals approximately 63.43 degrees, or 514394/8109This, as a polar coordinate, is (2sqrt5, (514394/8109))Using the polar system, however, you can express this point in infinitely many different ways. Just add/subtract 360 degrees to/from theta and you have the same point again.
