identity

Examples of identity in the following topics:

• Pythagorean Identities

  • The Pythagorean identities are useful in simplifying expressions with trigonometric functions.
  • Additional identities can be derived from the Pythagorean identity $\cos^2 t + \sin^2 t = 1$.
  • For example, if we divide the identity by $\cos^2 x$, we have the following identity:
  • Likewise, if we divide the identity by $\sin^2 x$, we have the following:
  • Recall that one of the Pythagorean identities states $1 + \tan^2 x = \sec^2 x$.

• Gender Identity in Everyday Life

  • Gender identity is one's sense of one's own gender.
  • Gender identity is one's sense of being male, female, or a third gender.
  • Gender identity is socially constructed, yet it still pertains to one's sense of self.
  • Transsexuals, however, take drastic measures to assume their believed identity.
  • Sociologists tend to emphasize the environmental impetuses for gender identity.

• Identity Formation

  • An example of national identity is the way in which Americans are united on the Fourth of July.
  • Indeed, the holiday would make little sense if one did not possess a sense of national identity.
  • An example of religious identity would be if someone identifies as belonging to a particular religious faith.
  • Individuals gain a social identity and group identity by their affiliations.
  • Cultural identity is one's feeling of identity affiliation to a group or culture.

• Socioemotional Development in Adolescence

  • Adolescence is the period of life known for the formation of personal and social identity.
  • Erik Erikson referred to the task of the adolescent as one of identity versus role confusion.
  • Three general approaches to understanding identity development include self-concept, sense of identity, and self-esteem.
  • Erikson determined that "identity achievement" resolves the identity crisis in which adolescents must explore different possibilities and integrate different parts of themselves before committing to their chosen identity.
  • Other cognitive developments have an impact on identity formation as well.

• Trigonometric Symmetry Identities

  • This symmetry is used to derive certain identities.
  • Notice that only two of the trigonometric identities are even functions: cosine and secant.
  • For these functions, we apply $f(-x) = f(x)$ to find the following identities:
  • For the odd trigonometric functions, we apply $f(-x) = -f(x)$ and find the following identities:
  • Explain the trigonometric symmetry identities using the graphs of the trigonometric functions

• The Identity Matrix

  • The matrix that has this property is referred to as the identity matrix.
  • The identity matrix, designated as $[I]$, is defined by the property: $[A][I]=[I][A]=[A]$.
  • so $\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$ is the identity matrix for $2 \times 2$ (square) matrices.
  • Why is there no identity for a non-square matrix?
  • There is no identity for a non-square matrix, because of the requirement of matrices being commutative.

• Development of Gender Identity

  • Gender identity is a person's subjective experience of their own gender; how it develops is a topic of much debate.
  • Studies suggest that children develop gender identity in three distinct stages:
  • Around age 5–7, gender identity becomes rigid in a process known as consolidation.
  • According to proponents of queer theory, gender identity is not a rigid or static identity but can continue to evolve and change over time.
  • The formation of gender identity is influenced by social factors, such as family.

• Race and Ethnicity

  • An individual is usually externally classified (meaning someone else makes the classification) into a racial group rather than the individual choosing where they belong as part of their identity.
  • Conceptions of race, as well as specific racial groupings, are often controversial due to their impact on social identity and how those identities influence someone's position in social hierarchies (see identity politics).Ethnicity, while related to race, refers not to physical characteristics but social traits that are shared by a human population.

• Beats

  • The superposition of two waves of similar but not identical frequencies produces a pulsing known as a beat.
  • The culprit is the superposition of two waves of similar but not identical frequencies.
  • This varying loudness occurs because the sound waves have similar but not identical frequencies.
  • Beats are produced by the superposition of two waves of slightly different frequencies but identical amplitudes.The waves alternate in time between constructive interference and destructive interference, giving the resulting wave a time-varying amplitude.

• Gender as a Spectrum and Transgender Identities

  • This social dichotomy enforces conformance to the ideals of masculinity and femininity in all aspects of gender and sex—gender identity, gender expression, and biological sex.
  • The gender continuum (sometimes referred to as the gender matrix) is an extension of this gender spectrum that includes additional gender identities.
  • The continuum approach to gender identity provides individuals with more personal freedom in which to express themselves.
  • The umbrella of transgender identities includes many different and sometimes-overlapping categories.
  • In addition, people may identify as androgynous, bigender, pangender, ambigender, non-gendered, agender, intergender, third gender, or another identity altogether.