Solving Trig Equations

Front

What is the Pythagorean identity for sine and cosine?

Back

sin²(x) + cos²(x) = 1

Front

What is the range of the sine function?

Back

[-1, 1]

Front

What is the range of the cosine function?

Back

[-1, 1]

Front

What is the secant function in terms of cosine?

Back

sec(x) = 1/cos(x) (where cos(x) ≠ 0)

Front

What is the cosecant function in terms of sine?

Back

csc(x) = 1/sin(x) (where sin(x) ≠ 0)

Front

What is the tangent function in terms of sine and cosine?

Back

tan(x) = sin(x)/cos(x) (where cos(x) ≠ 0)

Front

What is the cotangent function in terms of sine and cosine?

Back

cot(x) = cos(x)/sin(x) (where sin(x) ≠ 0)

Front

How do you solve the equation cos²(x) + sin(x) + 1 = 0?

Back

This equation has no solution in the interval [0, 2π) because cos²(x) + sin(x) + 1 is always positive.

Front

What is the solution to the equation 1/2sec(x) - 1 = 0?

Back

x = π/3, 5π/3

Front

What is the solution to the equation 4sin²(x) = 3?

Back

x = π/3, 2π/3, 4π/3, 5π/3