Mathematics: Geometry and Trigonometry Flashcards

What is the general solution of sin θ = √3/2 for 0° ≤ θ ≤ 360°?

Answer: 60° and 120°

sin θ = √3/2 gives θ = 60° (1st quadrant) and θ = 180° − 60° = 120° (2nd quadrant).

A cone has base radius 3 cm and slant height 5 cm. What is its curved surface area?

Answer: 15π cm²

Curved surface area = πrl = π(3)(5) = 15π cm².

Lines y = 2x + 3 and y = −(1/2)x + 1 are:

Answer: Perpendicular

Their slopes are 2 and −1/2; since 2 × (−1/2) = −1, the lines are perpendicular.

Express 210° in radians.

Answer: 7π/6

210° × (π/180°) = 210π/180 = 7π/6 radians.

In triangle PQR, the sine rule states that:

Answer: p/sin P = q/sin Q = r/sin R

The sine rule: p/sin P = q/sin Q = r/sin R, relating each side to the sine of its opposite angle.

A sphere has radius 3 cm. What is its surface area?

Answer: 36π cm²

Surface area of a sphere = 4πr² = 4π(9) = 36π cm².

Which identity is correct?

Answer: 1 + tan²θ = sec²θ

Dividing sin²θ + cos²θ = 1 by cos²θ gives tan²θ + 1 = sec²θ.