Trigonometry and the Unit Circle Flashcards

In a right triangle, the side opposite a 30° angle is 5. What is the length of the hypotenuse?

Answer: 10

sin(30°) = opposite/hypotenuse = 1/2. So hypotenuse = opposite ÷ sin(30°) = 5 ÷ (1/2) = 10.

What is the value of cos(60°)?

Answer: 0.5

cos(60°) = 1/2 = 0.5. This is a standard value from the unit circle / 30-60-90 triangle.

Which of the following is equivalent to tan(θ)?

Answer: sin(θ)/cos(θ)

By definition, tan(θ) = opposite/adjacent = (opposite/hypotenuse)/(adjacent/hypotenuse) = sin(θ)/cos(θ).

An angle of 3π/2 radians is equivalent to how many degrees?

Answer: 270°

Multiply by 180/π: (3π/2) × (180/π) = (3 × 180)/2 = 270°.

A ladder leans against a wall making a 65° angle with the ground. The ladder is 10 feet long. How high up the wall does it reach? (sin 65° ≈ 0.906)

Answer: 9.06 feet

The height (opposite side) = hypotenuse × sin(65°) = 10 × 0.906 = 9.06 feet.

Which of the following is a Pythagorean identity?

Answer: sin²(θ) + cos²(θ) = 1

sin²(θ) + cos²(θ) = 1 is the fundamental Pythagorean identity derived from the Pythagorean theorem applied to the unit circle.