Precal Final Review

Front

What is the Half-angle formula for sine?

Back

sin(θ/2) = ±√((1 - cos(θ))/2)

Front

Calculate sin 22.5º using the Half-angle formula.

Back

sin 22.5º = √(2 - √2)/2

Front

What are polar coordinates?

Back

A pair of numbers (r, θ) that represent a point in the plane, where r is the distance from the origin and θ is the angle from the positive x-axis.

Front

How do you convert polar coordinates to Cartesian coordinates?

Back

(x, y) = (r cos(θ), r sin(θ))

Front

What is the standard form of a hyperbola?

Back

(x-h)²/a² - (y-k)²/b² = 1 or (y-k)²/a² - (x-h)²/b² = 1

Front

Identify the conic section: 36x² – 5y² + 8x + 2y + 12 = 0.

Back

Hyperbola

Front

What is the formula for the components of a vector?

Back

A vector v = has components x and y.

Front

Find the components of the vector <5, 8.7>.

Back

The components are 5 and 8.7.

Front

What is the general equation of a circle?

Back

(x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.

Front

Write the equation of a circle with radius 2 and center (3, 4).

Back

(x-3)² + (y-4)² = 4