C2 - Radians Trig

Question 1

2.1.1 What are radians?

What distinguishes them from degrees?

Answer 1

Radians are a way of measuring angles, like degrees.

Radians use ratios of pi to measure angles. Radians are therefore more accurate as pi is the ration of the circumference to the diameter of a circle, and so they have a significant value. Degrees are, for the most part, an arbitrary measurement.

Question 2

2.1.2 Why do you hate degrees when learning about radians?

Answer 2

Because degrees is a shitty little measurement and can honestly go die why the fuck did we have to use them for our entire lives then get introduced to an actually useful method of measurement? Bullshit that’s why

Question 3

2.1.3 How to convert degrees to radians (and vice versa).

Answer 3

Deg to rad: degrees * (pi/180)

Rad to deg: rad * (180/pi)

Question 4

2.1.4 Normal formulae and radians.

Answer 4

Normal formulae, such as sine rule and area of a triangle, can be computed using radians as normal. If using a calculator, remember to switch mode from degrees to radians.

Question 5

2.1.5 Arc length formula (radians).

Area of sector formula (radians).

Area of segment formula (radians).

Answer 5

Radius * angle in rad

1/2 * radius^2 * angle in rad

1/2 * radius^2 * (angle - sin(angle))

Question 6

2.1.6 Trig graphs and radians.

Answer 6

Trig graphs can easily be given in radians rather than in degrees. It is easy to remember how to sketch the curve, remembering 180 deg = pi rad (360 deg = 2pi rad).

Question 7

2.1.7 Trig equations and radians.

Answer 7

The Trig equations discussed in the previous Trig deck will work just as well with radians, so long as you change more from degrees to radians.