The name of the shape graphed by the function r = 1 + 3 sin theta is known as a "heart" shape.
Which trigonometric functions are positive in which quadrant?
In first quadrant (0 < θ < π/2), all six trigonometric functions are positive.
In the second quadrant(π/2 < θ < π), only sin and cosec are positive.
In the third quadrant (π < θ < 3π/2), only tangent and cotangent are positive.
In fourth (3π/2 < θ < 2π = 0), only cos and sec are positive.
r = 1 + 3 sin(θ)
here θ is measured from the x-axis
when θ = 0, we have r = 1 (so we have a radius of 1 over the x-axis)
when θ = π/2, we have r = 1 + 3sin(π/2) = 4
when θ =π, we have r = 1 + 3sin(π) = 1
when θ = 3π/2, we have r = 1 + 3sin(3π/2) = -2
First, we have symmetry around the y-axis,
The value of x in θ = 0, θ = π and θ = 3π/2 is the same. so this is not a circle, this is actually a circle where the bottom part is flatted.
because between θ = π and θ = 2π are in the negative y-axis, so in this region, we have two small bumps that connect in the point (0, 0)
Learn more about trigonometric ratios here:
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