Cosine Ratio
Adjacent over hypotenuse.
Key idea
Adjacent over hypotenuse.
In depth
cos θ = adjacent / hypotenuse. It is the sine of the complementary angle: cos θ = sin(90° − θ). On the unit circle, cos θ is the x-coordinate.
Worked example
For a 3-4-5 triangle, cos of the angle opposite 3 is 4/5 = 0.8.
Formula
Real-world uses
- Finding how far a ladder reaches along a wall
- Resolving a force into horizontal parts
Common mistake
Mixing up sin and cos. Remember SOH-CAH-TOA.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Cosine Ratio?
Adjacent over hypotenuse. It is a topic at the intermediate level in Trigonometry.
What is the formula for Cosine Ratio?
The key formula is cosθ = adj/hyp.
Where is Cosine Ratio used in real life?
Real-world examples: Finding how far a ladder reaches along a wall; Resolving a force into horizontal parts.
What should I learn before Cosine Ratio?
Make sure you are comfortable with Sine Ratio, the previous topic in Trigonometry.
What is a common mistake with Cosine Ratio?
Mixing up sin and cos. Remember SOH-CAH-TOA.
How can I practise Cosine Ratio?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Cosine Ratio?
Move on to Tangent Ratio next.
Related intermediate topics in Trigonometry
- Radians – Angle measured by arc length on a unit circle; 2π rad = 360°.
- Converting Degrees and Radians – Multiply by π/180 or 180/π.
- Sine Ratio – Opposite over hypotenuse.
- Tangent Ratio – Opposite over adjacent.
- Reciprocal Trig Functions – Cosecant, secant and cotangent.
- Solving Right Triangles – Find all sides and angles using ratios and the Pythagorean theorem.