Right Triangle Trig Flashcard

Front

What is the definition of cosine in a right triangle?

Back

Cosine (cos) of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

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

Back

Tangent (tan) of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

Front

If cos(θ) = \frac{3}{5}, what is the value of sin(θ)?

Back

Using the Pythagorean identity: sin(θ) = \sqrt{1 - cos^2(θ)} = \sqrt{1 - \left(\frac{3}{5}\right)^2} = \frac{4}{5}.

Front

What is the Pythagorean theorem?

Back

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): a^2 + b^2 = c^2.

Front

How do you find the value of x in a right triangle if you know the lengths of the other two sides?

Back

Use the Pythagorean theorem: x = \sqrt{a^2 + b^2}.

Front

What is the value of tan(θ) if sin(θ) = \frac{3}{5} and cos(θ) = \frac{4}{5}?

Back

tan(θ) = \frac{sin(θ)}{cos(θ)} = \frac{\frac{3}{5}}{\frac{4}{5}} = \frac{3}{4}.

Front

What is the relationship between sine, cosine, and tangent?

Back

tan(θ) = \frac{sin(θ)}{cos(θ)}.

Front

If sin(X) = \frac{28}{41}, what is cos(X)?

Back

Using the Pythagorean identity: cos(X) = \sqrt{1 - sin^2(X)} = \sqrt{1 - \left(\frac{28}{41}\right)^2} = \frac{41}{41}.

Front

What is the value of sin(30°)?

Back

sin(30°) = \frac{1}{2}.

Front

What is the value of cos(60°)?

Back

cos(60°) = \frac{1}{2}.