Mathematics: Geometry and Trigonometry Flashcards

If sin θ = 0.6 and θ is in the first quadrant, what is cos θ?

Answer: 0.8

cos θ = √(1 − sin²θ) = √(1 − 0.36) = √0.64 = 0.8.

A cylinder has radius 4 cm and height 10 cm. What is its volume?

Answer: 160π cm³

Volume = πr²h = π(16)(10) = 160π cm³.

Two sides of a triangle are 7 and 10, and the included angle is 60°. Using the cosine rule, what is the third side?

Answer: √79

c² = 7² + 10² − 2(7)(10)cos60° = 49 + 100 − 70 = 79, so c = √79.

What is the period of the function y = sin(2x)?

Answer: π

The period of y = sin(bx) is 2π/b = 2π/2 = π.

Point P divides segment AB such that AP:PB = 2:3. If A = (0,0) and B = (10,5), what are the coordinates of P?

Answer: (4, 2)

P = (0 + 2/(2+3)·10, 0 + 2/(2+3)·5) = (4, 2).

The area of an equilateral triangle with side length s is:

Answer: (√3/4)s²

Area of an equilateral triangle = (√3/4)s², derived using height h = (√3/2)s.

Which of the following is equivalent to cos(180° − θ)?

Answer: −cos θ

Using the supplementary angle identity: cos(180° − θ) = −cos θ.