Eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = cos(t) + 5 y(t) = 7 sin2(t)

Answer 1

We use x(t) to solve for t and substitute the answer in y(t):

Find t.

x = cos(t) + 5,

cos(t) = x - 5,

t = arccos(x-5).

We simply substitute in y(t).

y = 7sin(2arccos(x - 5)).

We can now use trig identities to transform this into algebraic equation

a) double angle formula first

y = 7 x 2 x sin(arccos(x - 5)) cos(arccos(x-5))

b) using sin(arccos(x)) = √(1 - x²) and cos(arccos(x)) = x, we get

y = 14 (x - 5)√(1 - (x - 5)²)

In case you have interpretation that 2 is an exponent, even simpler - use Pythagorean identity for sine and cosine:

y = 7sin²(arccos(x - 5))

y = 7[1 - cos²(arccos(x - 5))]

y = 7[ 1 - (x - 5)²]