Trigonometric Ratios

Summary and Exam Tips for Trigonometric Ratios

Trigonometric Ratios is a subtopic of Geometry and Trigonometry, which falls under the subject Mathematics in the IB MYP curriculum. In a right-angled triangle, the hypotenuse is the side opposite the right angle and is the longest side. The opposite side is across from a given angle, while the adjacent side is the non-hypotenuse side next to the angle. The primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan), defined for an acute angle $A$ as follows:

• $\sin(A) = \frac{\text{opposite}}{\text{hypotenuse}}$
• $\cos(A) = \frac{\text{adjacent}}{\text{hypotenuse}}$
• $\tan(A) = \frac{\text{opposite}}{\text{adjacent}}$

A helpful mnemonic to remember these ratios is SOH-CAH-TOA. Trigonometric ratios are used to find unknown sides and angles in right-angled triangles. For example, if one angle and one side are known, the third angle can be found using the angle sum property of triangles (180°), and trigonometry can be applied to calculate the other sides. Practical applications include solving problems like determining the height of a flagpole based on its shadow and the angle of the sun's rays.

Exam Tips

• Understand the Triangle: Always start by correctly identifying the hypotenuse, opposite, and adjacent sides relative to the given angle.
• Memorize SOH-CAH-TOA: This mnemonic is crucial for quickly recalling the definitions of sine, cosine, and tangent.
• Practice Problem-Solving: Work through various examples to become comfortable with using trigonometric ratios to find unknown sides and angles.
• Check Units and Angles: Ensure all measurements are in the correct units and angles are in degrees unless specified otherwise.
• Use Diagrams: Drawing a clear diagram can help visualize the problem and identify the sides and angles correctly.