Trigonometric Ratios

Summary

Trigonometric ratios are used to relate the angles and sides of right-angled triangles. These ratios help in calculating unknown sides or angles when certain measurements are known.

• Hypotenuse — the side opposite the right angle and the longest side in a right triangle. Example: In triangle ABC, if angle C is 90°, then side AB is the hypotenuse.
• Opposite Side — the side across from a given angle in a right triangle. Example: In triangle ABC, if angle A is the reference angle, then side BC is the opposite side.
• Adjacent Side — the non-hypotenuse side that is next to a given angle. Example: In triangle ABC, if angle A is the reference angle, then side AC is the adjacent side.
• Sine (sin) — the ratio of the length of the opposite side to the hypotenuse. Example: sin(A) = opposite/hypotenuse
• Cosine (cos) — the ratio of the length of the adjacent side to the hypotenuse. Example: cos(A) = adjacent/hypotenuse
• Tangent (tan) — the ratio of the length of the opposite side to the adjacent side. Example: tan(A) = opposite/adjacent
• SOH-CAH-TOA — a mnemonic to remember the definitions of sine, cosine, and tangent. Example: SOH (Sine = Opposite/Hypotenuse), CAH (Cosine = Adjacent/Hypotenuse), TOA (Tangent = Opposite/Adjacent)

Exam Tips

Key Definitions to Remember

• Hypotenuse is the longest side opposite the right angle.
• Opposite side is across from the given angle.
• Adjacent side is next to the given angle and not the hypotenuse.
• Sine, cosine, and tangent are ratios of sides in a right triangle.

Common Confusions

• Mixing up the opposite and adjacent sides relative to different angles.
• Forgetting that the hypotenuse is always the longest side.

Typical Exam Questions

• What is the sine of angle A? Use sin(A) = opposite/hypotenuse.
• How do you find the length of the hypotenuse? Use the Pythagorean theorem or trigonometric ratios.
• How do you calculate an unknown angle? Use inverse trigonometric functions.

What Examiners Usually Test

• Ability to correctly label the sides of a right triangle.
• Application of SOH-CAH-TOA to solve problems.
• Understanding of how to find unknown sides or angles using trigonometric ratios.