Secant of Angle plus Full Angle

Theorem

$\sec \left({x + 2 \pi}\right) = \sec x$

Proof

\(\ds \sec \left({x + 2 \pi}\right)\)

\(=\)

\(\ds \frac 1 {\cos \left({x + 2 \pi}\right)}\)

Secant is Reciprocal of Cosine

\(\ds \)

\(=\)

\(\ds \frac 1 {\cos x}\)

Cosine of Angle plus Full Angle

\(\ds \)

\(=\)

\(\ds \sec x\)

Secant is Reciprocal of Cosine

$\blacksquare$

Also see

• Sine of Angle plus Full Angle
• Cosine of Angle plus Full Angle
• Tangent of Angle plus Full Angle
• Cotangent of Angle plus Full Angle
• Cosecant of Angle plus Full Angle

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Functions of Angles in All Quadrants in terms of those in Quadrant I