How would you describe the curve?

Mathematics

1 answer:

erastovalidia [21]3 years ago

8 0

the answer is C, the curve is a one to one function

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Find the slope of the curve below at the given points. Sketch the curve along with its tangents at these points. R = sin 2 theta

mr Goodwill [35]

Answer:

-1 

Step-by-step explanation:

Given that:

r = sin 2θ , θ = ± π/4 , ± 3π/4

Recall that:

x = r cosθ

y = r sinθ

The differential of y with respect to x

$\dfrac{dy}{dx} = \dfrac{\dfrac{dy}{d \theta}}{\dfrac{dx}{d \theta}}$

$\dfrac{dy}{dx} =\dfrac{\dfrac{dy}{d \theta}}{\dfrac{dx}{d \theta}} = \dfrac{ r cos \theta + sin \theta* \dfrac{dr}{d \theta} } {\dfrac{dr}{d \theta} *cos \theta- sin \theta \ r}$

at θ = π/4 , r = sin π/2

r = 1

$\dfrac{dy}{dx} = \dfrac{ r cos \theta + 2 cos (2 \theta)*sin \ \theta } {2 \ cos (2 \theta) *cos \theta- sin 2 \theta * sin \theta}$

where;

θ = π/4

$\dfrac{dy}{dx} = \dfrac{ 1 \times cos (\dfrac{\pi}{4}) + 2 cos (\dfrac{\pi}{2})*sin (\dfrac{\pi}{4}) } {2 \ cos (\dfrac{\pi}{2})*cos (\dfrac{\pi}{4})- sin (\dfrac{\pi}{2}) * sin (\dfrac{\pi}{4})}$