Ch. 4 Trigonometric Functions Flashcard SOHCAHTOA

Front

What does SOHCAHTOA stand for in trigonometry?

Back

SOHCAHTOA 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

Define the sine function in a right triangle.

Back

The sine function (sin) of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

Front

Define the cosine function in a right triangle.

Back

The cosine function (cos) of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

Define the tangent function in a right triangle.

Back

The tangent function (tan) of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

Front

If the opposite side of a right triangle is 3 and the hypotenuse is 5, what is the sine of the angle?

Back

sin(θ) = Opposite/Hypotenuse = 3/5 = 0.6.

Front

If the adjacent side of a right triangle is 4 and the hypotenuse is 5, what is the cosine of the angle?

Back

cos(θ) = Adjacent/Hypotenuse = 4/5 = 0.8.

Front

If the opposite side of a right triangle is 3 and the adjacent side is 4, what is the tangent of the angle?

Back

tan(θ) = Opposite/Adjacent = 3/4 = 0.75.

Front

What is the Pythagorean theorem?

Back

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

Front

How do you find the length of the hypotenuse if the lengths of the other two sides are 6 and 8?

Back

Using the Pythagorean theorem: c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10.

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, which are consistent for similar triangles.