Give the center and radius of the circle generated by the equations x = 3 sin t, y = -3 cos t, for 0 ≤ t ≤ 2π. Specify the direction of positive orientation.

Q: Find the points of intersection of the graphs of the equations r = 1 + sin θ,       r = 3 sin θ

A: r = 1 + sin θ,       r = 3 sin θ To find: The points of intersection of the graphs of the equations.

Q: Show that the point is on the unit circle. (-똥) V5 2 3 '3/

A:

Q: Plot the curve r = 1+sin 8. Then find the length of the curve.

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Q: dx v16+x? 2) Use a trigonometric substitution to help integrate: Clearly show what your values of x…

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Q: show that r = cos 2θ is symmetrical with respect to the horizontal axis.

A: show that r = cos 2θ is symmetrical with respect to the horizontal axis.

Q: Direction: differentiate the following: 5x 4. tan 5. у -sin(6x'-1)

A: 4. Let y=tan5x4 ⇒dydx=ddxtan5x4⇒dydx=sec25x4×ddx5x4⇒dydx=sec25x4×54dxdx⇒dydx=54sec25x4

Q: 2 sin z = 4+51

A:

Q: Name three different pairs of polar coordinates that also name the point, (-1,-), if-2 ≤ 0 ≤ 2π

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Q: For each point given in rectangular coordinates, write three different polar representations of the…

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Q: For Cartesian coordinates (x,y)=(1, -√3), find the angle in the polar coordinates in radians.

A: Use the formula for angle in the polar coordinates.

Q: Draw a right angled triangle with another angle θ such that sinθ = 5 13. Find tan(θ) from this…

A: Assume that triangle ABC is a right angle triangle and angle B is 90 degree.

Q: d. Inside the circle r=4 sine and below the horizontal line r= 3 csce

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Q: L Find the six trigonometric function of the following 2)(4) 1) (4, 4) Ans. Ans.

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Q: Write an equation of the line tangent to this curve at point A r = −8 sin(θ)  polar coordinate…

A: Given query is to find the equation of the tangent line

Q: -0.5 0.5+ -0.5+ r 0.5

A: Angle measured in clockwise direction is negative and angle measured in anti-clockwise direction is…

Q: Determine an equation for the sinusoidal function shown: vv (-4x/3, 2) (141/3, 2) 14n (5ェ3, 4)

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Q: from Evaluate cos r sin x dr.

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Q: 2. Draw a triangle that you would need the tangent function to solve. Don't forget to indicate where…

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Q: the rectangular equation if r = 4 cos 0 + 4 sin 0

A: Given query is is to find the rectangular equation.

Q: Determine two equations (one cosine and one sine) for the sinusoidal graph below. Show your work…

A: NOTE: Refresh your page if you can't see any equations. . assume that the sine function is in the…

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.