Trigonometry Beyond Right Triangles · Overview

Trigonometry Beyond Right Triangles

These questions start where SOH-CAH-TOA stops. You convert between degrees and radians, find arc lengths, read sine and cosine from the unit circle, give the sign of a trig value in any quadrant, and simplify expressions with identities such as sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1.

Others work with triangles that have no right angle, using the law of sines or the law of cosines, or with the graphs of sine and cosine: amplitude, period, midline, and maximum and minimum values. Every question has four choices. ACT's test descriptions don't list a formula sheet, so know the common formulas; in this course, the less common ones, such as the two laws, are given in the stem.

How often it appears

Trigonometry sits inside the Geometry and Functions categories of Preparing for Higher Math, each 17–20% of the Math section. These questions are quick points once the facts are familiar.

You have 50 minutes for 45 questions, about 67 seconds each. Knowing the exact values, the quadrant signs, and the period formula by heart is what keeps these questions well under a minute.

The question you’ll see

What is the period of the function f(x)=3sin⁡(4x)+1f(x) = 3\sin(4x) + 1?

In this module

  1. Overview Paid
  2. Radians and the unit circle Paid
  3. Trig values in every quadrant Paid
  4. Identities you can use Paid
  5. Law of sines and law of cosines Paid
  6. Sine and cosine graphs Paid
  7. Strategy summary Paid
  8. Mastery quiz Paid
  9. Pace check Paid