Trigonometry and coordinate geometry

Question 1 of 10

Simplify (1 − cos²θ)/sin θ.

Question 2 of 10

Given sin 3θ = 3 sin θ − 4 sin³θ, find sin 3θ when sin θ = 1/2.

Question 3 of 10

Find the gradient of the line perpendicular to y = 2x + 5.

Question 4 of 10

If tan A = 3/4 (A acute), find sin 2A.

Question 5 of 10

Express √3 sin θ + cos θ in the form R sin(θ + α).

Question 6 of 10

cos 75° expressed exactly is

Question 7 of 10

The centre of the circle x² + y² − 4x + 6y − 3 = 0 is

Question 8 of 10

Find the equation of the circle with centre (2, −1) and radius 3.

Question 9 of 10

Find the centre of the circle x² + y² − 4x + 6y − 3 = 0.

Question 10 of 10

The gradient of the line joining (1, 2) and (3, 8) is