Solving Trig Equations

Front

What is the Pythagorean identity for sine and cosine?

Back

sin²x + cos²x = 1

Front

How do you factor the equation 0 = sin²x - sinx?

Back

0 = sinx(sinx - 1)

Front

What is the solution to the equation 1/4sin x + 1 = 0 on the domain [0, 2π)?

Back

No solution

Front

What is the factored form of sec²x - secx - 2?

Back

(secx - 2)(secx + 1)

Front

How do you solve the equation 2sin x cos x = √2 cos x?

Back

Divide by cos x (if cos x ≠ 0) to get 2sin x = √2, then solve for x.

Front

What is the general solution for sin x = 0?

Back

x = nπ, where n is an integer.

Front

What is the general solution for cos x = 0?

Back

x = (2n + 1)π/2, where n is an integer.

Front

What is the double angle formula for sine?

Back

sin(2x) = 2sin(x)cos(x)

Front

What is the double angle formula for cosine?

Back

cos(2x) = cos²(x) - sin²(x) or cos(2x) = 2cos²(x) - 1 or cos(2x) = 1 - 2sin²(x) depending on the context.

Front

What is the range of the sine function?

Back

[-1, 1]