Title: Trigonometry - Fundamental Trigonometric Identities - dialogCards (Rep, NoAdv)

Authors: Justine Leon Uro (Author)
Licence: CC BY 4.0

FUNDAMENTAL TRIGONOMETRIC IDENTITIES

Complete each of the following indentities.

Q: \( \cos^2 x + \sin^2 x = \underline{\;\;?\;\;}\)
A: \( 1 \)
  Hint: A Pythagorean Identity
  Hint: A fixed constant

Q: \( 1 + \tan^2 x = \underline{\;\;?\;\;}\)
A: \( \sec^2 x \)

Q: \( \cot^2 x + 1 = \underline{\;\;?\;\;}\)
A: \( \csc^2 x \)
  Hint: A Pythagorean Identity

Q: \(\tan x = \displaystyle \frac{\;\;\;?\;\;\;}{?}\)
A: \(\displaystyle \frac{\;\; \sin x \;\;}{\cos x}\)
  Hint: Definition of the tangent function

Q: \(\cot x = \displaystyle \frac{\;\;\;?\;\;\;}{?}\)
A: \(\displaystyle \frac{\; \cos x \;}{\; \sin x \;}\)
  Hint: Definition of the cotangent function
  Hint: 1/tan x is also correct

Q: \(\sec x = \displaystyle\frac{\;\;\;?\;\;\;}{?}\)
A: \(\displaystyle \frac{1}{\; \cos x \;}\)
  Hint: Definition of the secant function

Q: \(\csc x = \displaystyle\frac{\;\;\;?\;\;\;}{?}\)
A: \(\displaystyle \frac{\; 1\;}{\; \sin x \;}\)
  Hint: Definition of the cosecant function

Q: \( \tan x \cot x = \underline{\;\;?\;\;}\)
A: \(1\)
  Hint: A reciprocal identity