2.Make a sketch of the following polar equation: r = 2 +4 sin 0 (r, 0). Determine also the tangent gradient of the polar curve at the point with 0 = "/2

Eliminate the parameter in the parametric equations x =7+ sint, y = 2 + sint, for 0sts and describe the curve, indicating its positive orientation. How does this curve differ from the curve x = 7+ sin t, y = 2 + sin t, for 7stsn?

Use the parametric equations x= sec(t) , y=tan(t), for -pi/2 < t < pi/2. Sketch the curve represented by the parametric equations (include the orientation of the curve) and write the corresponding rectangular equation by eliminating the parameter and Find the equation of the tangent line to the curve at t = pi/4

Trace the curve r² = 4cos⁴(theta) tan²(theta).

Given the polar function r = f(theta) = 4sin(2*theta) Find the average rate of change of "f" between 3pi/4 and pi, and use that rate of change to estimate the value of "r" for theta= 5pi/6

Consider the curve described by the parametric equations ¤ = t² +4 and y = 3t + 4t. Determine the slope of the tangent line to the curve when t = 1. Enter your answer as an exact value in decimal form.

Plot the following curves in polar coordinates. 1. r = 2 + cos (50) 2 2. r = sin 0 + sin³ (5) 2 3. resin 0 4. r r = sin() 5. r= 1 + cos 50 6. r² sin 0 = - - 7. r = 3 + 2 cos 0 8. r = √6 9. r 9 sin 0 3 10.r = 2 cos 0

Evaluate;

Find the equation of the osculating plane of the curve (a sin u + b cos , a cos u + b sin 44, c sin 2 u ) Bo S

Consider the polar curve with equation r=1+2cos(θ):   (I) The slope of the tangent line to the curve at θ=π/3 is √3 / 9(II) The curve has no vertical tangent lines.   which is false or true