Understanding Basic Trigonometric Identities: Reciprocal, Quotient, and Pythagorean Identities
This guide covers fundamental trigonometric identities essential for solving various mathematical problems. It includes definitions of reciprocal identities (e.g., sin A = 1/csc A), quotient identities (e.g., tan A = sin A/cos A), and Pythagorean identities (e.g., sin² A + cos² A = 1). Additionally, practical examples demonstrate these identities in action, providing clarity on their applications. Enhance your understanding of trigonometry and improve your problem-solving skills with these foundational concepts.
Understanding Basic Trigonometric Identities: Reciprocal, Quotient, and Pythagorean Identities
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Presentation Transcript
By: Kristina Kennedy, Colin Schamp, and Jess Bello Basic Trigonometric Identities
Reciprocal Identities • SIN A= 1/csc A • COS A= 1/sec A • TAN A= 1/cot A • CSC A= 1/sin A • SEC A=1/cos A • COT A= 1/tan A
Quotient Identities • TAN A= sin A/cos A (y/x) • COT A= cosA/ sin A (x/y)
Pythagorean Identities • 1+Cot²x=Csc²x • Tan²x+1=Sec²x • Sin²x+Cos²x=1 • Sin ²=1-Cos²x • Cos²x=1-Sin²x
Examples Example 1: Example 2: • sinA×cotA • sinA×(cosA/sinA) • =cosA • cosA(secA-cosA) • cosA((1/cosA)-(cosA/1)) • 1-cos²A • =sin²A
