Answer:
1/32v²sin2θ
Step-by-step explanation:
Given the expression r(theta) = 1/16v²sinθcosθ
According to double angle of trigonometry identity;
Sin2θ = sin(θ+θ)
Sin2θ = sinθcosθ + cosθsinθ
Sin2θ = 2sinθcosθ
sinθcosθ = sin2θ/2 ... **
Substituting equation ** into the question
1/16v²sinθcosθ = 1/16v²(sin2θ/2)
1/16v²sinθcosθ = 1/2×1/16v²(sin2θ)
1/16v²sinθcosθ = 1/32v²sin2θ
Hence using the double angle identity, the equivalent expression is 1/32v²sin2θ
Let's find the derivative of that hyperbola in order to find a slope formula to help us with this equation. We already have an x and y value. The derivative is found this way:
so
. The derivative supplies us with the slope formula we need to write the equation. Sub in the x value of 3 to find what the slope is:
. So in our slope-intercept equation, x = 3, y = 1, and m = -1/3. Use these values to solve for b.
so b = 2. The equation, then, for the line tangent to that hyperbola at that given point is
Since the absolute value of any number is always positive, the absolute value of -2 2/3 is 2 2/3.
Hope this helps!