Trigonometric Identities and Transformations
The Pythagorean, compound-angle, multiple-angle and product-to-sum identities relate trigonometric functions of related angles.
What is Trigonometric Identities and Transformations?
The Pythagorean, compound-angle, multiple-angle and product-to-sum identities relate trigonometric functions of related angles.
Key formula / rule: sin2 t + cos2 t = 1 with its tangent and cotangent variants.
Key points
- Derive compound-angle identities from the unit circle.
- Apply identities to simplify trigonometric expressions.
Common exam trap
Applying an identity outside the domain where the functions are defined.
Definitions
- Term
Trigonometric Identities and Transformations
- Meaning
The Pythagorean, compound-angle, multiple-angle and product-to-sum identities relate trigonometric functions of related angles.
- Term
Trigonometric Identities and Transformations — explanation
- Meaning
Identities are the grammar of trigonometry: every simplification is a controlled rewriting. Knowing which family to reach for is the difference between two lines and two pages.
Learning objectives
Derive compound-angle identities from the unit circle.
Apply identities to simplify trigonometric expressions.
Formulae
- Key point
sin2 t + cos2 t = 1 with its tangent and cotangent variants.
- Key point
Compound-angle formulae generate all multiple-angle results.
- Key point
Product-to-sum formulae linearise products for integration.
Common mistakes
Applying an identity outside the domain where the functions are defined.
Losing the sign when the angle lies outside the first quadrant.
Keywords
Trigonometric
Identities
Transformations
Practice preview
What is the value of sin^2(theta) + cos^2(theta)?…
easy
The maximum value of 3sin(x) + 4cos(x) is:…
hard
If sin(A) = 3/5 and A is in the first quadrant, what is the value of sin(2A)?…
easy