##### 9.5 ASTC rule in trigonometry (All Students Take Calculus)

Trigonometry comes from two Greek words that translate to triangle and measure.Trigonometry basically tackles all about measuring a triangle, most especially the right triangles. If you remember our discussion previously about Pythagorean Theorem, then you would have fully grasped the core of trigonometry.

Pythagorean Theorem is summarized by the equation $a^2 + b^2 = c^2$, where a and b are both sides of the right triangle, and c is the hypotenuse (or the longest side of the right triangle). From our previous discussion chapter, we know that Trigonometry utilizes the six trigonometric functions. To remember them, we use the mnemonic SOH-CAH-TOA which stands for sine-opposite-hypotenuse, cosine-adjacent-hypotenuse and tangent-opposite-adjacent. We will also look at the ASTC way to solve Trigonometric ratios.

Also we will be tackling the angles involved in trigonometry like standard angle, co-terminal angles and the reference angles. Standard angles are basically angles formed by a ray and the x axis. The x axis is the initial arm and the other ray would be the terminal arm. The angle formed from the initial side to the terminal side is the standard angle. Co-terminal angles on one hand are angles that have the same initial and terminal sides. One of the angles would have a positive measurement while the other would have negative measurement. The other angle is the reference angle and this is the angle formed by the terminal side of another angle and the x- axis. We will also have a brief look at the special angles of Trigonometry like the 45-45-90 angles, the 30-60-90 angles, and the 60-60-60 angles.

This chapter would also discuss all about the unit circle. In this chapter we will learn that unit circles are basically just circles in the quadrant and have a radius that has a measure of 1 unit. We can be able to investigate unit circles with graphing calculators to understand them more. We will get to apply this concept as well as the other concepts we have here with some mathematical problems.

### ASTC rule in trigonometry (All Students Take Calculus)

###### 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