Geometry and Trigonometry Flashcards

In a right triangle, sin(θ) is defined as which ratio?

Answer: opposite/hypotenuse

By SOHCAHTOA, sine equals the ratio of the opposite side to the hypotenuse.

What is the value of cos(60°)?

Answer: 1/2

cos(60°) = 1/2 is a standard unit circle value.

What does the Pythagorean trigonometric identity state?

Answer: sin²(θ) + cos²(θ) = 1

The fundamental Pythagorean identity is sin²(θ) + cos²(θ) = 1 for all angles θ.

If tan(θ) = 1 and 0° < θ < 90°, what is θ?

Answer: 45°

tan(45°) = 1 because sin(45°) = cos(45°) = √2/2, making their ratio equal to 1.

A 10-foot ladder leans against a wall making a 60° angle with the ground. How high up the wall does it reach?

Answer: 5√3 feet

sin(60°) = height/10, so height = 10 × (√3/2) = 5√3 feet.

How many degrees are equivalent to 2π radians?

Answer: 360°

One full revolution equals 2π radians = 360°.

Which of the following is equivalent to cos(30°)?

Answer: √3/2

cos(30°) = √3/2 is a standard unit circle value derived from the 30-60-90 triangle.