Solving Trig Equations

Front

Define the cosine function in terms of a right triangle.

Back

In a right triangle, the cosine of an angle θ is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

What is the range of the cosine function?

Back

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

Front

Solve for θ: cos(θ) = 0.5 on θ∈[0, 2π).

Back

θ = π/3, 5π/3.

Front

What is the sine function in terms of a right triangle?

Back

In a right triangle, the sine of an angle θ is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

Front

What is the range of the sine function?

Back

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

Front

Solve for θ: sin(θ) = √(3)/2 on θ∈[0, 2π).

Back

θ = π/3, 2π/3.

Front

Define the tangent function in terms of sine and cosine.

Back

The tangent function is defined as tan(θ) = sin(θ)/cos(θ).

Front

What is the period of the sine and cosine functions?

Back

The period of the sine and cosine functions is 2π.

Front

Solve for θ: tan(θ) = 0 on θ∈[0, 2π).

Back

θ = 0, π, 2π.

Front

What is the relationship between the angles in a right triangle?

Back

The sum of the angles in a right triangle is 180 degrees (or π radians), with one angle being 90 degrees (or π/2 radians).