Trigonometric Ratios
Sine, cosine, and tangent
lessons (4)
Introduction to Trigonometric Ratios
Learn the three fundamental trigonometric ratios (sine, cosine, tangent) and the SOH-CAH-TOA mnemonic.
Sine Ratio (SOH)
Master the sine ratio and learn how to find missing sides and angles using opposite and hypotenuse.
Cosine Ratio (CAH)
Master the cosine ratio and learn how to find missing sides and angles using adjacent and hypotenuse.
Tangent Ratio (TOA)
Master the tangent ratio and learn how to find missing sides and angles using opposite and adjacent.
Trigonometric ratios relate the angles of a right triangle to the ratios of its sides. The three primary ratios - sine (opposite/hypotenuse), cosine (adjacent/hypotenuse), and tangent (opposite/adjacent) - allow us to find unknown sides and angles in right triangles. The mnemonic SOH-CAH-TOA helps remember these relationships.
These ratios extend far beyond triangles. They describe periodic phenomena like sound waves, light waves, and seasonal patterns. Trigonometry is essential in physics, engineering, architecture, music, and any field involving waves, rotations, or cyclical patterns. Understanding the basic ratios is the first step into this powerful mathematical framework.
What Students Will Learn
- Define sine, cosine, and tangent ratios
- Use SOH-CAH-TOA to find missing sides
- Use inverse trig functions to find angles
- Solve right triangle problems
- Apply trigonometry to real-world situations
Frequently Asked Questions
What does SOH-CAH-TOA mean?
SOH: Sine = Opposite/Hypotenuse. CAH: Cosine = Adjacent/Hypotenuse. TOA: Tangent = Opposite/Adjacent. This mnemonic helps remember which sides to use for each ratio.
What is the difference between sin and sin inverse?
Sin takes an angle and gives a ratio. Sin inverse (arcsin) takes a ratio and gives an angle. Use sin to find sides; use sin inverse to find angles.
Why are trig ratios the same for all similar triangles?
Similar triangles have the same angles and proportional sides. Since trig ratios depend only on the angle (not the size), any triangle with the same angle has the same ratio values.