Trigonometry guides
Calculate angles, triangle sides, and master trigonometric functions with our comprehensive guides.
11 guides · each with a free step-by-step calculator
Sine Rule Calculator: Complete Guide to Solving Triangles with the Law of Sines
How do surveyors measure the width of a river without crossing it? They measure one distance and two angles, then let the sine rule do the rest. In this guide you'll learn the sine rule, when to use it instead of the cosine rule, and how to avoid the tricky 'ambiguous case'.
Cosine Rule Calculator: Solve Triangles Using the Law of Cosines
You already know Pythagoras: a² + b² = c². But what if the triangle has no right angle? The cosine rule is Pythagoras with a correction term that works for every triangle. In this guide you'll learn the formula, how to find a side or an angle with it, and the sign mistake that catches almost everyone.
Sine Rule vs Cosine Rule: How to Choose Which Formula to Use (With Decision Guide & Worked Examples)
Solving a non-right triangle is one of the most common stumbling blocks in high school and college trigonometry. Should you reach for the Sine Rule or the Cosine Rule? The choice comes down to what three pieces of information you already have. This guide provides a simple decision framework, complete formulas, and fully worked examples so you never pick the wrong rule again.
Law of Cosines: Find a Side From SAS (Explained)
You hike 8 km on one trail, turn, then hike 10 km on another trail at a 50° angle from the first. How far is the straight-line walk back to camp? The Law of Cosines answers that for any triangle, right-angled or not.
How to Convert Degrees to Radians
Why does a 90° turn become 1.5708 in your coding project's math library? Because most programming languages and calculus formulas use radians, not degrees. This guide shows you the one-line conversion.
How to Convert Radians to Degrees
A sensor reports that a door swung open by "2 radians" — but what does that actually look like? Converting back to degrees turns an abstract number into an angle you can picture, in one short calculation.
Partner Spotlight
How to Find Sin, Cos, and Tan of an Angle
A ladder leans against a wall at a 45° angle — but what does that angle actually tell you about the ladder's height and distance from the wall? Sine, cosine, and tangent turn a single angle into three useful ratios.
What Is Inverse Trig? Finding Angles From a Ratio
A wheelchair ramp rises 0.5 meters for every meter of hypotenuse — but what angle is that, exactly? Inverse trig functions turn a known ratio back into the angle that produced it.
Double Angle Formula for Sine (sin 2θ)
An engineer already worked out sin(20°) and cos(20°) for a signal calculation — does she really need to start over to get sin(40°)? No. The double angle formula reuses what she already has.
Double Angle Formula for Cosine (cos 2θ)
A physicist has already measured sin(20°) and cos(20°) for a wave calculation — can she get cos(40°) without measuring the doubled angle directly? Yes, with one more identity built from what she already knows.
Triangle Area From Two Sides and an Angle (SAS)
A garden plot has two fence sides of 6 and 9 meters meeting at a 40° angle, but no way to measure straight up from the ground. How do you find its area without ever finding the height?
