# What is the area enclosed by #r=-cos(theta-(7pi)/4) # between #theta in [4pi/3,(5pi)/3]#?

The graph is a circle of radius 1/2, through pole, with center on

graph{(sqrt2(x^2+y^2)+x+y)(y+sqrt3x)(y-sqrt3x)=0 [-2.5, 2.5, -1.25, 1.25]}

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To find the area enclosed by ( r = -\cos\left(\theta - \frac{7\pi}{4}\right) ) between ( \theta = \frac{4\pi}{3} ) and ( \theta = \frac{5\pi}{3} ), you integrate ( \frac{1}{2} r^2 ) with respect to ( \theta ) from the lower bound to the upper bound. The integral will yield the desired area.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the area enclosed by #r=-thetasin(-16theta^2+(7pi)/12) # between #theta in [0,(pi)/4]#?
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- What is the distance between the following polar coordinates?: # (2,(23pi)/12), (3,(7pi)/8) #
- What is the Cartesian form of #( 2 , ( - 15pi)/2 ) #?

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