(1 point) A curve with polar equation r = 5 sin 0 + 36 cos 0 represents a line. This line has a Cartesian equation of the form y = mx + b ,where m and b are constants. Give the formula for y in terms of x. For example, if the line had equation y = 2x + 3 then the answer would be 2 * x + 3.
Convert the following equation to Cartesian coordinates. Describe the resulting curve. r= - 8 cos 0-6 sin 0 Write the Cartesian equation. Describe the curve. Select the correct choice below and, if necessary, fill in any answer box O A. The curve is a circle centered at the point with radius (Type exact answers, using radicals as needed.) B. The curve is a vertical line with x-intercept at the point (Type exact answers, using radicals as needed.) O C. The...
- cos Transform the polar equation to an equation in rectangular coordinates. Then identity and graph the equation, Write an equation in rectangular coordinates. (Type an equation) What is the graph of this equation? O A horizontal line c. circle with center at(-4,0) OB. vertical line OD. circle with center at (4,0) Select the graph of -8cos e ОА Ов, Ос. OD Click to select your answers
Graph the polar equation r=6 sin 30 OD Convert the Cartesian equation to a polar equation that expresses r in terms of e. (x + 3)² + y² = 9 = (Type an expression in terms of 0.)
Use the graph of the parabola to fill in the table. (a) Does the parabola open upward or downward? 61 41 u O upward downward (b) Find the coordinates of the vertex. 2+ -10 - 10 vertex: OD -4 -6 -10 (c) Find the intercept(s). For both the x- and y-intercept(s), make sure to do the following. • If there is more than one, separate them with commas. • If there are none, select "None". x-intercept(s): 0 y-intercept(s): 0 (d)...
(1 point) A curve with polar equation r = 27 8 sin 0 + 49 cos 0 represents a line. This line has a Cartesian equation of the form y = mx +b ,where m and b are constants. Give the formula for y in terms of x. For example, if the line had equation y = 2x + 3 then the answer would be 2 *x+3. Hint: multiply both sides by the denominator on the right hand side and...
7) The graph of r = Sin 2θ is given in both rectangular and polar coordinates. Identify the points in (B) corresponding to the points A-I in (A), with corresponding intervals.8) Describe the graph of: r = a Cos θ + b Sin θ 9) Write the equation, in polar coordinate, of a line with (2, π/9) 5 the closest point to the origin.
3. (18 points) Consider the polar equation r = 2 + 2 cos(0). Describe the graph of this equation. What is it's axis of symmetry? How would you change the equations to make this a limaçon with an inner loop?
Convert the polar equation to rectangular form and sketch its graph. r = 7 cot(0) csc(O) Step 1 The polar coordinates (r, e) of a point are related to the rectangular coordinates (x, y) of the point as follows. x=rcos(0) cos y = r sin(0) sin e Step 2 The given polar equation can be rewritten as follows. r 7 cote csco 1 r = 7 coto sino 2 sin(0) = 7 coto Converting to rectangular coordinates using x =...
is shown cos 7x- cos 9x The graph with the equation y sin 7x + sin 9x in a [0,2xx] by [-2.2.1) viewing rectangle a. Describe the graph using another equation b. Verify that the two equations are equivalent D a. Write another equation of the given graph (Type an equation using x as the variable) b. To verify that the two equations are equal, start with the numerator of the right side and apply the appropriate sum-to product formula...