Study Notes
Trigonometric ratios are used to relate the angles and sides of right-angled triangles. The three main trigonometric ratios are sine, cosine, and tangent, which are defined for acute angles in a right triangle.
- 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 is opposite over hypotenuse.
- Cosine is adjacent over hypotenuse.
- Tangent is opposite over adjacent.
Common Confusions
- Mixing up the opposite and adjacent sides.
- Forgetting which side is the hypotenuse.
- Confusing the ratios for sine, cosine, and tangent.
Typical Exam Questions
- What is the sine of angle A in a right triangle? Use sin(A) = opposite/hypotenuse.
- How do you find the length of a side using cosine? Use cos(A) = adjacent/hypotenuse.
- How do you calculate an angle using tangent? Use tan(A) = opposite/adjacent.
What Examiners Usually Test
- Ability to correctly label sides of a right triangle.
- Correct use of trigonometric ratios to find unknown sides or angles.
- Understanding and application of SOH-CAH-TOA.