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Lesson Example Discussion Quiz: Class Homework

Lesson

Title: Trigonometry Identities ( Pythagorean, reciporcal)

Grade: 10-a Lesson: S3-L3

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. Pythagorean identities
2. Reciprocal identities

$1$

Explanation: In trigonometry, a right triangle contains a 90-degree angle. Its sides are designated based on their connection to this angle: the hypotenuse, opposite, and adjacent sides, each playing a distinct role.

Definition: Pythagorean identities

Pythagorean identities in trigonometry are a set of equations that relate the three basic trigonometric functions: sine (sin⁡), cosine (cos⁡), and tangent (tan⁡).

$2$

Explanation:

\$sin^2(x) + cos^2(x) = 1\$
\$1+tan^2(x) = sec^2(x)\$
\$1+cot^2(x) = csc^2(x)\$

Definition: Reciprocal identities

Reciprocal identities in trigonometry involve the reciprocals of the three primary trigonometric functions: sine (sin⁡), cosine (cos⁡), and tangent (tan⁡). These identities express the relationship between each trigonometric function and its reciprocal.

$3$

Explanation:

\$csc(x) = 1/(sin(x))\$
\$sec⁡(x) = 1/(cos⁡(x))\$
\$cot⁡(x) = 1/(tan⁡(x))\$