Assessment: Trigonometry

In Quadrant III, which trigonometric ratio is positive?

At which of these angles is tan θ undefined?

Given sin θ = 0.28 and θ is in Quadrant I, find cos θ.

In triangle JKL, angle J = 90°, angle K = 30°, and side j = 20. Find side k.

In triangle ABC, a = 5, b = 12, and angle C = 90°. Find side c.

Find sin 300° using the basic acute angle. (Give your answer to 3 decimal places.)

A plane flies 100 km on a bearing of 070°, then turns and flies 100 km on a bearing of 160°. What is the interior angle of the flight path at the turning point?

A surveyor measures two sides of a triangular plot as 40 m and 25 m, with a 90° angle between them, but cannot measure the height directly. Which formula should they use for the area?

Why does the Law of Cosines reduce exactly to the Pythagorean theorem when C = 90°?

Given tan θ = 3/4 and θ is in Quadrant III (where both sin and cos are negative), find sin θ.