Trigonometry

Trigonometry studies the relationships between angles and side lengths in triangles, extending these ratios to functions defined on the unit circle. This topic covers basic trig ratios (sine, cosine, tangent), verifying and applying identities, solving trig equations, inverse trig functions, and the law of sines and cosines.

Trigonometry is fundamental to navigation, surveying, astronomy, music theory, and any field that involves waves, oscillations, or angular measurements.

Practice Tips

• 1Learn the unit circle values for 0, pi/6, pi/4, pi/3, and pi/2 in both radians and degrees, since most problems use these reference angles.
• 2When verifying identities, work on one side only (usually the more complicated side) and transform it to match the other using known identities.
• 3For equations like sin(x) = c, find all solutions in one full period first, then add 2 pi n (or 360 n) to capture the general solution.