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 other two sides are labeled based on their relation to a given angle: the opposite side is across from the angle, while the adjacent side is next to the angle but not the hypotenuse.

The trigonometric ratios are the ratios of these sides and include sine ($\sin$), cosine ($\cos$), and tangent ($\tan$). These are 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 mnemonic to remember these ratios is SOH-CAH-TOA. Trigonometric ratios are useful for finding unknown sides or angles in right-angled triangles. For example, if one angle and one side are known, the third angle can be determined using the angle sum property of triangles, and the other sides can be calculated using trigonometry.

Exam Tips

• Understand the Triangle: Always start by correctly identifying the hypotenuse, opposite, and adjacent sides relative to the angle in question.

• Memorize SOH-CAH-TOA: This mnemonic is crucial for quickly recalling the definitions of sine, cosine, and tangent.

• Practice Problem Solving: Work through various problems to become comfortable with using trigonometric ratios to find unknown sides and angles.

• Check Your Angles: Remember that the sum of angles in a triangle is $180^\circ$. Use this to verify your calculations.

• Use Real-world Examples: Apply trigonometric ratios to real-world scenarios, like calculating heights and distances, to better understand their practical applications.