# ASTC rule in trigonometry (**A**ll **S**tudents **T**ake **C**alculus) - Trigonometric Ratios and Angle Measures

## Trigonometry ASTC

When you work with trigonometry, you’ll be dealing with four quadrants of a graph. The x and y axis divides up a coordinate plane into four separate sections.

ASTC is a memory-aid for memorizing whether a trigonometric ratio is positive or negative in each quadrant: [Add-Sugar-To-Coffee]

When you draw it out, it looks like this:

You can even use this diagram as a trigonometry cheat sheet. ASTC will help you remember how to reconstruct this diagram so you can use it when you’re met with trigonometry quadrants in your test questions.

In the above graphic, we have quadrant 1 2 3 4. In quadrant 1, both x and y are positive in value. In quadrant 2, x is negative while y is still positive. In quadrant 3, both x and y are negative. Lastly, in quadrant 4, x is positive while y is negative.

What this tells us is that if we have a triangle in quadrant one, sine, cosine and tangent will all be positive. In quadrant two, only sine will be positive while cosine and tangent will be negative. See how this is an easy way to allow you to remember which trigonometric rations will be positive?

If you don’t like Add Sugar To Coffee, there’s other acronyms you can use such as:

All Students Take Calculus

All Stations To Central

Better yet, if you can come up with an acronym that works best for you, feel free to use it. As long as it contains ASTC in that order, you’ll remember the trig quadrants.

If you wanted to look further into trigonometric ratios, why not take a look and revise how the sine graph is graphed. You can also see how the cosine and tangent graphs look and what information you can get out of them.

### ASTC rule in trigonometry (**A**ll **S**tudents **T**ake **C**alculus)

###### Basic concepts:

- Use sine ratio to calculate angles and side (Sin = $\frac{o}{h}$ )
- Use cosine ratio to calculate angles and side (Cos = $\frac{a}{h}$ )
- Use tangent ratio to calculate angles and side (Tan = $\frac{o}{a}$ )

###### Related concepts:

- Sine graph: y = sin x
- Cosine graph: y = cos x
- Tangent graph: y = tan x