Inverse Trig Ratios

Front

What is the definition of inverse trigonometric functions?

Back

Inverse trigonometric functions are functions that determine the angle whose trigonometric ratio is a given number. They include sin^-1, cos^-1, and tan^-1.

Front

What is the relationship between sine and its inverse?

Back

If sin(θ) = x, then θ = sin^-1(x).

Front

What is the relationship between cosine and its inverse?

Back

If cos(θ) = x, then θ = cos^-1(x).

Front

What is the relationship between tangent and its inverse?

Back

If tan(θ) = x, then θ = tan^-1(x).

Front

What is the range of the inverse sine function?

Back

The range of sin^-1(x) is [-π/2, π/2] or [-90°, 90°].

Front

What is the range of the inverse cosine function?

Back

The range of cos^-1(x) is [0, π] or [0°, 180°].

Front

What is the range of the inverse tangent function?

Back

The range of tan^-1(x) is (-π/2, π/2) or (-90°, 90°).

Front

How do you remember the trigonometric ratios?

Back

Use the mnemonic 'Soh Cah Toa': Soh = sin = opposite/hypotenuse, Cah = cos = adjacent/hypotenuse, Toa = tan = opposite/adjacent.

Front

What is the formula to find an angle using tangent?

Back

To find an angle θ, use θ = tan^-1(opposite/adjacent).

Front

If sin(θ) = 3/5, what is θ?

Back

θ = sin^-1(3/5) or approximately 36.87°.