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The graph of the curve represented by {x=sec(theta) and y=cos(theta)} is what?
Also if you can these two are really tough for me as well-
if x,3x+3,5x+5 are three consecutive terms of a geometric sequence, then the sum of these three terms is?
The graph of the curve is represented by {3sin(theta) and y=3sin(theta)} is?
1 Answer
- No MythologyLv 78 years agoFavorite Answer
If x = secΘ and y = cosΘ, then y = 1/x. So you get part of a hyperbola. But -1 ≤ y ≤ 1 and |x| ≥ 1. So letting Θ vary over all reals, you'd pick up the parts of the hyperbola y = 1/x from the point (1, 1) down toward the x-axis, and the part coming from under the x-axis (x->-∞ and y -> 0) down to the point (-1, -1).
(3x + 3)/x = (5x + 5)/(3x + 3) ==> (3x + 3)² = x(5x + 5) ==>
9x² + 18x + 9 = 5x² + 5x ==> 4x² + 13x + 9 = 0 ==> (4x + 9)(x + 1) = 0.
Now x can not equal -1 since this would give 3x + 3 = 0---and zero can't be in geometric progression with -1. So that leaves x = -9/4.
x + (3x + 3) + (5x + 5) = -49/4 when x = -9/4.
If x = 3sinΘ and y = 3sinΘ, then y = x. So the parametric curve is part of this line. Given the properties of the sine function -3 ≤ x, y ≤ 3. So you get the part of the line y = x from (-3, -3) to (3, 3).
