Introduction to Trigonometry
Trigonometry explores relationships between the angles and sides of right-angled triangles. The three main ratios - sine, cosine, and tangent - allow us to calculate unknown sides and angles.
What You Need to Know
Key Concept Diagram
In a right-angled triangle, sides are labelled relative to an angle: Opposite, Adjacent, Hypotenuse
SOH: sin(angle) = Opposite / Hypotenuse
CAH: cos(angle) = Adjacent / Hypotenuse
TOA: tan(angle) = Opposite / Adjacent
The mnemonic SOH-CAH-TOA helps remember the three trigonometric ratios
Key Vocabulary
Sine (sin)
The ratio of the opposite side to the hypotenuse in a right-angled triangle
Cosine (cos)
The ratio of the adjacent side to the hypotenuse in a right-angled triangle
Tangent (tan)
The ratio of the opposite side to the adjacent side in a right-angled triangle
Hypotenuse
The longest side of a right-angled triangle, always opposite the right angle
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
In a right-angled triangle, what does SOH-CAH-TOA represent?
Question 2
In a right-angled triangle, the side opposite to angle A is 6 cm and the hypotenuse is 10 cm. What is sin(A)?
Question 3
Which ratio uses the Adjacent and Hypotenuse sides?
Key Concepts Summary
- ●In a right-angled triangle, sides are labelled relative to an angle: Opposite, Adjacent, Hypotenuse
- ●SOH: sin(angle) = Opposite / Hypotenuse
- ●CAH: cos(angle) = Adjacent / Hypotenuse
- ●TOA: tan(angle) = Opposite / Adjacent
- ●The mnemonic SOH-CAH-TOA helps remember the three trigonometric ratios