What you’ll learn
Understand sine, cosine and tangent.
Key idea
Use opposite/hypotenuse, adjacent/hypotenuse and opposite/adjacent for sine, cosine and tangent respectively.
Opposite/adjacent depend on the reference angle; common scaling cancels in every trig ratio.
Worked example
Classify examples and non-examples for the concept 'Understand sine, cosine and tangent'.
A right triangle has opposite=36, adjacent=15, hypotenuse=39 relative to acute theta. Select the complete valid ratio classification.
- For this angle the opposite, adjacent and hypotenuse are 36, 15, 39.
- Applying the definitions gives sin(theta)=12/13, cos(theta)=5/13, tan(theta)=12/5.
Answer: sin(theta)=12/13, cos(theta)=5/13, tan(theta)=12/5 — each numerator and denominator follows its definition.
Quick Check
Classify examples and non-examples for the concept 'Understand sine, cosine and tangent'.
A right triangle has opposite=21, adjacent=20, hypotenuse=29 relative to acute theta. Select the complete valid ratio classification.