Secant of Zero

Theorem

$\sec 0 = 0$

where $\sec$ denotes secant.

Proof

\(\ds \sec 0 \degrees\)

\(=\)

\(\ds \frac 1 {\cos 0 \degrees}\)

Secant is Reciprocal of Cosine

\(\ds \)

\(=\)

\(\ds \frac 1 1\)

Cosine of Zero is One

\(\ds \)

\(=\)

\(\ds 1\)

$\blacksquare$

Also see

• Sine of Zero is Zero
• Cosine of Zero is One
• Tangent of Zero
• Cotangent of Zero
• Cosecant of Zero

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles