Compound, Double & Sub-Multiple Angles explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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Compounngle formulae help find trigonometric values of combined angles.
They are used when an angle is written as a sum, difference, double, or half of another angle.
This topic supports identities, equations, calculus, and advanced problem solving.
A compound angle is made by adding or subtracting angles.
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Compounngle formulae give correct expansion rules.
Doublngle formulae are special cases where both angles are the same.
Halngle formulae help when an expression contains 1 plus or minus cos A.
Meaning: An angle such as or .
Definition: Compounngle formulae express ratios of or using ratios of A and B.
Use these when angles are split into known standard angles.
Meaning: These handle .
Definition: The signs change according to the ratio.
For sine, subtraction gives sin A cos os A sin B.
Meaning: A double angle is 2A.
Definition: Doublngle formulae come from putting .
They simplify expressions such as sin 2A and cos 2A.
Meaning: These involve half angles such as .
Definition: Halngle formulae express ratios of using cos A.
They are useful for exact values and transformations.
Easy
Question: Write sin 2A using sin A and cos A.
Medium
Question: Find sin 75 degrees using 45 degrees and 30 degrees.
Exam-level
Question: Simplify cos 2A using only sin A.
Writing in in B
Why it happens: The angle operation is confused with value operation.
Correct approach: Use the full compounngle formula.
Using the wrong sign in cosine formula
Why it happens: Sine and cosine patterns are mixed.
Correct approach: Cos() has a minus sign between the products.
Ignoring quadrant signs for half angles
Why it happens: Only the squaroot part is considered.
Correct approach: Check the quadrant before choosing plus or minus.
Can I add sine values directly?
No. Use the compounngle formula.
Where do doublngle formulae come from?
They come from compounngle formulae with both angles equal.
Why do halngle formulae need signs?
Square roots can be positive or negative depending on the quadrant.
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