Answer: 8x^2 + 2y^2 = 7
Explanation:
The equation R = 7/8cosθ + 2sinθ can be rewritten in terms of x and y using the conversions x = Rcosθ and y = Rsinθ.
Substituting R = 7/8cosθ + 2sinθ into these equations, we get:
x = (7/8)cosθ cosθ + 2sinθ cosθ
y = (7/8)cosθ sinθ + 2sinθ sinθ
Simplifying these expressions using trigonometric identities, we get:
x = (7/8)cos^2θ + (4/8)sin2θ
y = (7/8)sinθ cosθ + (4/8)sin2θ
Multiplying both sides of the x equation by 8/7 and simplifying, we obtain:
8x^2 + 2y^2 = 7cos^2θ + 8sin^2θ
Using the identity cos^2θ + sin^2θ = 1, we get:
8x^2 + 2y^2 = 7(1)
Therefore, the Cartesian form of the equation is 8x^2 + 2y^2 = 7.