Trigonometry
Compare sine, cosine and tangent using right triangles and the unit circle. Then vary the angle to explore the relationships.
Right-triangle ratios
1 comparison · No time limit · Explore after checking
Example
Example
Compare two right-triangle ratios.
Review the comparison
The triangle is right-angled. Its hypotenuse c is 8 units.
45° < θ < 90°.
Side a is opposite θ; side b is adjacent to θ.
The picture shows one allowed acute angle. The right angle and hypotenuse stay fixed.
a ÷ c (sin θ)
b ÷ c (cos θ)
Choose an answer to try the example.
Why?
Explore the relationship
Make the adjacent leg b exactly half the hypotenuse.
In this drawing
Need a clue?
The adjacent-to-hypotenuse ratio is cos θ. Look for cos θ = 1/2.
Example positions
Change θ within the given range. The legs adjust while c remains fixed.
The controls preserve the givens. Examples illustrate the rule; the explanation proves it.
Go further Apply the idea
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How this data is usedHelp
Choose whether Quantity A is greater, Quantity B is greater, the quantities are equal, or the relationship cannot be determined. Use only the stated givens. A drawing shows one possible case.
Your first checked answer counts. A shown answer counts as 0 correct. A checked comparison is saved immediately, so you can explore afterward without losing your result. An unfinished comparison is not saved as a result.
After checking, use the controls to solve an exploration goal. When the relationship cannot be determined, save two valid cases with different comparisons. Open Go further to apply the idea to a new question. These activities are optional and do not change your score.
Angles and trigonometric functions use degrees. Levels increase the mathematical complexity; they do not measure IQ.
About this practice
Learn a method
Choose a triangle ratioCompare sine, cosine and tangent using right triangles and the unit circle. Then vary the angle to explore the relationships.
For a broader mix of practices, explore the geometry practice test. Membership is required to start a test.
Report a problem
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is used