Trigonometry - Finding missing angles

Front

What is the definition of SOH CAH TOA?

Back

SOH CAH TOA is a mnemonic for remembering the definitions of the sine, cosine, and tangent functions in a right triangle: SOH = Sine = Opposite/Hypotenuse, CAH = Cosine = Adjacent/Hypotenuse, TOA = Tangent = Opposite/Adjacent.

Front

How do you find a missing angle using inverse trigonometric functions?

Back

To find a missing angle, use the inverse trigonometric functions: sin⁻¹, cos⁻¹, or tan⁻¹, depending on the sides of the triangle you have. For example, if you know the opposite and hypotenuse, use sin⁻¹.

Front

If sin(θ) = 0.5, what is θ?

Back

θ = 30° or 150° (in degrees), since sine is positive in the first and second quadrants.

Front

If cos(θ) = 0.6, what is θ?

Back

θ = 53.1° or 306.9° (in degrees), since cosine is positive in the first and fourth quadrants.

Front

If tan(θ) = 1, what is θ?

Back

θ = 45° or 225° (in degrees), since tangent is positive in the first and third quadrants.

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 range of the tangent function?

Back

The range of the tangent function is all real numbers (-∞, ∞).

Front

How do you round an angle to the nearest tenth?

Back

To round an angle to the nearest tenth, look at the hundredths place. If it is 5 or more, round up; if it is less than 5, round down.

Front

If you have a right triangle with an opposite side of 5 and a hypotenuse of 10, what is the angle θ?

Back

θ = sin⁻¹(5/10) = sin⁻¹(0.5) = 30°.