Assessment: Trigonometry

What does SOH-CAH-TOA help you remember?

From what reference line is the angle of elevation always measured?

Convert 270° to radians.

A circle has radius 12. Find the arc length for a central angle of 0.5 radians.

If sinθ = 8/17 and θ is acute, find cosθ. (Give as a fraction's numerator over 17 — just the numerator.)

In a right triangle, the hypotenuse is 20 and one acute angle is 53°. Find the side adjacent to that angle. (cos53° ≈ 0.602. Round to 1 decimal place.)

A sprinkler waters a circular sector of radius 5 m, rotating through 1.2 radians. Find the watered area.

From a point 60 m from a building's base, the angle of elevation to its top is 40°. Find the building's height. (tan40° ≈ 0.839. Round to the nearest metre.)

Why do sin(30°) and cos(60°) have exactly the same value?

In a right triangle, tanθ = 5/12. Find secθ (the hypotenuse over the adjacent side), as a fraction's numerator over 12 (just the numerator — hint: this is a 5-12-13 triangle).