# Difference between Geometry and Trigonometry?

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9 years ago

The standard high school math curriculum in the US is:

1) Algebra 1

2) Geometry

3) Algebra 2

4) Precalculus aka Trigonometry aka Analytic Geometry

5) AP Calculus (either AB for one semester of college credit, or BC for two semesters of credit)

*) AP Statistics (Technically doable after Algebra 2 typically, but you really should ensure that you complete calc first if you intend to take any advanced physics. More of an "elective" than standard.)

Not everything that's taught in "Algebra 1" or "Algebra 2" is algebra, strictly speaking. There may be sections on data analysis, basic intro to statistics, discrete mathematics / combinatoric topics, and other stuff.

As far as trigonometry goes, literally speaking it is the measaure (-metry) of triangles (trig-). It involves three special functions...sine, cosine, and tangent. In your first geometry class, between algebra 1 and 2, you'll typically learn basic right triangle trig. You'll learn how to compute sines and cosines of 30, 45, and 60 degrees, as well as how to use a calculator/table to find measures of sides/angles in right triangles. You might even learn how to resolve vectors into x and y components.

In "trig" class, you expand your definition of sine and cosine. In geometry, sine was "opposite/hypotenuse". In "trig", you find the sine of an angle by:

1) Drawing an angle with the +x axis as one of the sides, and revolving COUNTER-clockwise. You can have this angle be any degree measure you want...not just 0 to 90. You can have 180 degree angles, 270 degree angles....even 720 degree angles (which is really just 2 rotations, so you end right back where you wind up.)

2) Draw a unit circle.

3) Find where the ray intersects the unit circle. That point is (cos T, sin T), where T is the angle that you drew.

This unit circle definition is more flexible. You can't take the sine of 135 degrees with a right triangle, since you can't have a right triangle with a 135 degree angle. However, you can draw a 135 degree angle to the +x-axis, and you'll see that its sine is the same as the sine of 45. You'll also notice that its cosine is the OPPOSITE of the cosine fo 45.

Basically, the trigonometry class expands upon your old definitiions of sine, cosine, and tangent. But you don't just do trig in trigonometry class...you'll deal with logarithms, proofs (like inductiion), conic sections, and all sorts of other stuff. But it's typically taken two years after geometry.