Knowing the value of an arc we can calculate the value of the trigonometric functions (as a function of this arc): sine, cosine, tangent, cosecant, cotangent.
When we are working with the same angle (arc) the functions applied to that arc will form relationships with each other. See the main trigonometric relationships of functions with the same arc:
• Between the cosine, sine, cosecant of the same angle will obey the following relationship:
cog x = cos x
sin x
With x ≠ kπ, k 
Z.
• Between secant and cosine of the same angle will obey the following relationship:
sec x = 1
cos x
With x ≠ π + kπ Z.
2
• Between the cosecant and sine of the same angle will obey the following relationship:
cosec x = 1
sin x
With x ≠ k π, k Z.
• The relationship established between the tangent, the sine and the cosine, as long as the angles of the three trigonometric functions are equal, is:
tg x = sin x
cos x
With x ≠ π + kπ Z.
2
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by Danielle de Miranda
Graduated in Mathematics
Brazil School Team
Trigonometry - Math - Brazil School
Would you like to reference this text in a school or academic work? Look:
RAMOS, Danielle de Miranda. "Relationships between functions of the same arc"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/relacoes-entre-funcoes-mesmo-arco.htm. Accessed on June 27, 2021.
