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Lesson Example Discussion Quiz: Class Homework

Lesson

Title: Trigonometry Identities (quotient , co-function)

Grade: 10-a Lesson: S3-L4

Explanation: Hello students, let us learn a new topic in SAT-2 today with definitions, concepts, examples, and worksheets included.

Lesson:

Definition: Trigonometry Identities

Trigonometric identities are equations that involve trigonometric functions and are true for every value of the variables within their domains.
Some common trigonometric identities include:
1. Quotient identities
2. Co-function identities

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Explanation: These identities are fundamental in trigonometry and are used to simplify expressions, solve equations, and prove other mathematical statements involving trigonometric functions.

Definition: Quotient identities

Quotient identities involve ratios of trigonometric functions. The most commonly used quotient identities involve the sine, cosine, and tangent functions.

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Explanation: The quotient of sine and cosine is tangent.

\$"tan"("x") = ("sin"("x"))/("cos"("x"))\$
\$"cot"⁡("x") = ("cos"⁡("x"))/("sin"⁡("x"))\$

Definition: Co-function identities

Co-function identities relate the trigonometric functions of complementary angles \$("angles whose sum is 90 degrees or" π/2 "radians")\$.

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Explanation: Sine and Cosine Co-function Identity:

\$"sin"⁡π/(2 − θ) = cos⁡(θ)\$
\$"cos"⁡π/(2 − θ) = sin⁡(θ)\$
Tangent and Cotangent Co-function Identity:
\$"tan"⁡π/(2 − θ) = "cot"⁡(θ)\$
\$"cot"⁡π/(2 − θ) = "tan"⁡(θ)\$