Trigonometry

If cos(θ) = 4/5 and θ is acute, find sec(θ) and tan(θ).

If sin(θ) = 5/13 and θ is an acute angle, find cos(θ).

In a right triangle, the side adjacent to angle θ is 12 and the hypotenuse is 13. Find cos(θ).

In a right triangle, the side opposite angle θ is 6 and the hypotenuse is 10. Find sin(θ).

In a right triangle, the side opposite angle θ is 8 and the adjacent side is 15. Find tan(θ).

In triangle ABC, angle A = 40°, angle B = 65°, and side a = 12. Find side b to the nearest tenth.

In triangle ABC, sides a = 7 and b = 10 form an included angle C = 60°. Find side c to the nearest tenth.

Simplify the expression (1 - cos²(θ)) / sin(θ), assuming sin(θ) ≠ 0.

Solve 2sin(θ) = √3 for 0° ≤ θ < 360°.

Solve cos(θ) = -1/2 for 0° ≤ θ < 360°.