Solve Trig Equations

Front

What is the general solution of the equation sin(x) = 0?

Back

x = πn, where n is any integer.

Front

What is the general solution of the equation cos(x) = 0?

Back

x = π/2 + πn, where n is any integer.

Front

What is the general solution of the equation tan(x) = 0?

Back

x = πn, where n is any integer.

Front

What is the solution of sin(x) = 1 over the interval [0, 2π)?

Back

x = π/2.

Front

What is the solution of cos(x) = -1 over the interval [0, 2π)?

Back

x = π.

Front

What is the solution of tan(x) = 1 over the interval [0, 2π)?

Back

x = π/4; 5π/4.

Front

What is the general solution of the equation sin(x) = k, where -1 ≤ k ≤ 1?

Back

x = arcsin(k) + 2πn and x = π - arcsin(k) + 2πn, where n is any integer.

Front

What is the general solution of the equation cos(x) = k, where -1 ≤ k ≤ 1?

Back

x = arccos(k) + 2πn and x = -arccos(k) + 2πn, where n is any integer.

Front

What is the general solution of the equation tan(x) = k?

Back

x = arctan(k) + πn, where n is any integer.

Front

What is the solution of sin(x) = 0.5 over the interval [0, 2π)?

Back

x = π/6; 5π/6.