Equations that are true for all angles, used to simplify trigonometric expressions.
Basic trigonometric ratios: Understanding the three basic trigonometric ratios: sine, cosine and tangent, and how they are used in solving for unknown angles and sides in right triangles.
Unit circle: Understanding what a unit circle is and how it can be used to derive trigonometric identities.
Radian measure: Learning about radians as a measure of angles and how they relate to degrees.
Pythagorean theorem: Understanding how the Pythagorean theorem can be used to derive trigonometric ratios and identities.
Complementary angles: Learning about complementary angles and how they can be used to derive trigonometric identities.
Reciprocal, quotient, and co-function identities: Understanding the three common types of trigonometric identities and how they can be used in solving problems.
Addition and subtraction formulas: Learning about the addition and subtraction formulas for sine, cosine, and tangent and how they can be used to simplify trigonometric expressions.
Double angle identities: Learning about the double angle identities for sine, cosine, and tangent and how they can be used to simplify expressions involving trigonometric functions.
Half angle identities: Understanding the half angle identities for sine, cosine, and tangent and how they can be used to simplify expressions involving trigonometric functions.
Product-to-sum and sum-to-product identities: Learning about the product-to-sum and sum-to-product identities for sine and cosine and how they can be used to simplify expressions involving trigonometric functions.
Inverse trigonometric functions: Learning about the inverse trigonometric functions and how they can be used to solve equations involving trigonometric functions.
Applications of trigonometry: Understanding how trigonometry is used in real-world applications, such as in navigation, engineering and physics.
Pythagorean Identities: These are the most basic identities in trigonometry. They involve the relationship between the sides of a right triangle and are expressed in terms of sine, cosine, and tangent.
Reciprocal Identities: These identities are used to express trigonometric functions in terms of their reciprocals.
Quotient Identities: These are used to express the tangent and cotangent functions in terms of the sine and cosine functions, respectively.
Cofunction Identities: These identities describe the relationship between complementary angles. They show that the sine of an angle is equal to the cosine of its complementary angle, and the same is true for cosine and tangent, and secant and cosecant.
Even and Odd Identities: These identities describe the properties of trigonometric functions that are even or odd functions.
Sum and Difference Identities: These identities are used to express the sine, cosine, and tangent of the sum or difference of two angles in terms of the sine, cosine, and tangent of the individual angles.
Double Angle Identities: These identities are used to express the sine, cosine, and tangent of twice an angle in terms of the sine, cosine, and tangent of the angle.
Half Angle Identities: These identities are used to express the sine, cosine, and tangent of half an angle in terms of the sine, cosine, and tangent of the angle.
Product to Sum Identities: These identities are used to express the product of two trigonometric functions in terms of the sum or difference of those functions.
Sum to Product Identities: These identities are used to express the sum or difference of two trigonometric functions in terms of the product of those functions.
Inverse Trigonometric Identities: These identities are used to express the inverse trigonometric functions in terms of the original trigonometric functions.