Solving Trig Equations

Front

What is the range of the sine function?

Back

The range of the sine function is [-1, 1].

Front

What is the range of the cosine function?

Back

The range of the cosine function is [-1, 1].

Front

What is the period of the sine function?

Back

The period of the sine function is 2π.

Front

What is the period of the cosine function?

Back

The period of the cosine function is 2π.

Front

What is the cosecant function?

Back

The cosecant function is the reciprocal of the sine function: csc(θ) = 1/sin(θ).

Front

What is the secant function?

Back

The secant function is the reciprocal of the cosine function: sec(θ) = 1/cos(θ).

Front

How do you solve the equation 4sinθ + 1 = 3?

Back

Subtract 1 from both sides: 4sinθ = 2. Then divide by 4: sinθ = 1/2. The solutions in [0, 2π) are θ = π/6 and θ = 5π/6.

Front

How do you solve the equation 2cscθ + 2 = 0?

Back

Subtract 2 from both sides: 2cscθ = -2. Then divide by 2: cscθ = -1. The solution in [0, 2π) is θ = 3π/2.

Front

What does it mean if an equation has no solution?

Back

It means there are no values of the variable that satisfy the equation within the given interval.

Front

How do you solve the equation 2cosx - 4 = 0?

Back

Add 4 to both sides: 2cosx = 4. Then divide by 2: cosx = 2. Since the cosine function cannot equal 2, there is no solution.