Trigonometry

Front

What does SOH CAH TOA stand for in trigonometry?

Back

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

Front

How do you find the length of a side in a right triangle using trigonometric ratios?

Back

To find the length of a side in a right triangle, you can use the trigonometric ratios (sine, cosine, tangent) based on the known angle and the length of another side.

Front

What is the formula to calculate the sine of an angle?

Back

The sine of an angle is calculated as the ratio of the length of the opposite side to the length of the hypotenuse: sin(θ) = Opposite/Hypotenuse.

Front

What is the formula to calculate the cosine of an angle?

Back

The cosine of an angle is calculated as the ratio of the length of the adjacent side to the length of the hypotenuse: cos(θ) = Adjacent/Hypotenuse.

Front

What is the formula to calculate the tangent of an angle?

Back

The tangent of an angle is calculated as the ratio of the length of the opposite side to the length of the adjacent side: tan(θ) = Opposite/Adjacent.

Front

How can you find the measure of an angle if you know the lengths of two sides?

Back

You can use the inverse trigonometric functions: sin⁻¹, cos⁻¹, or tan⁻¹, depending on which sides you know. For example, if you know the opposite and hypotenuse, use sin⁻¹(Opposite/Hypotenuse).

Front

What is the Pythagorean theorem and how is it used in trigonometry?

Back

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): c² = a² + b². It is used to find the length of a side when the lengths of the other two sides are known.

Front

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

Back

In a right triangle, the angles determine the ratios of the lengths of the sides. The larger the angle, the longer the opposite side relative to the adjacent side.

Front

What is the significance of the 30-60-90 triangle in trigonometry?

Back

In a 30-60-90 triangle, the sides are in a specific ratio: 1 : √3 : 2. This means that if the shortest side (opposite the 30° angle) is x, the longer leg (opposite the 60° angle) is x√3, and the hypotenuse is 2x.

Front

What is the significance of the 45-45-90 triangle in trigonometry?

Back

In a 45-45-90 triangle, the sides are in the ratio 1 : 1 : √2. This means that if each leg is x, the hypotenuse is x√2.