Trig ratios

Front

What are the three primary trigonometric ratios?

Back

Sine (sin), Cosine (cos), and Tangent (tan).

Front

What does the acronym 'Soh Cah Toa' represent?

Back

It is a mnemonic to remember the definitions of the sine, cosine, and tangent ratios: Soh = sin = opposite/hypotenuse, Cah = cos = adjacent/hypotenuse, Toa = tan = opposite/adjacent.

Front

How do you find the height of an object using trigonometric ratios?

Back

You can use the sine ratio: height = distance from the object * sin(angle of elevation).

Front

If sin(θ) = opposite/hypotenuse, what is the value of the opposite side if the hypotenuse is 10 and θ is 30 degrees?

Back

The opposite side = 10 * sin(30°) = 10 * 0.5 = 5.

Front

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

Back

The ratios of the lengths of the sides are constant for given angles, which defines the trigonometric functions.

Front

How do you calculate the angle of elevation from a point to the top of an object?

Back

Use the tangent ratio: angle = arctan(opposite/adjacent).

Front

What is the cosine of 45 degrees?

Back

cos(45°) = √2/2 or approximately 0.707.

Front

What is the tangent of an angle in a right triangle?

Back

Tangent is the ratio of the length of the opposite side to the length of the adjacent side: tan(θ) = opposite/adjacent.

Front

How can you use trigonometric ratios to solve for an unknown side in a right triangle?

Back

Identify the known sides and the angle, then use the appropriate trigonometric ratio (sin, cos, or tan) to solve for the unknown side.

Front

What is the sine of 90 degrees?

Back

sin(90°) = 1.