What is the value of 3/2 sec(pi/3) ?

The value of 3/2 sec(pi/3) is 3

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3/2 sec(pi/3)

\frac{3}{2} sec (\frac{π}{3})

3

Solution steps

\frac{3}{2} sec (\frac{π}{3})

Use the following trivial identity:

sec (\frac{π}{3}) = 2

sec (\frac{π}{3})

sec (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

= \frac{3}{2} \cdot 2

Simplify

\frac{3}{2} \cdot 2 : 3

\frac{3}{2} \cdot 2

Convert element to fraction:

2 = \frac{2}{1}

= \frac{3}{2} \cdot \frac{2}{1}

Cross-cancel:

2

= \frac{3}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 3

= 3

cot (- \frac{π}{12})

arcsin (\frac{2}{8})

tan (\frac{37 π}{4}) + sec (\frac{175 π}{4})

sin (arccos (- \frac{2}{3}) + 2 arctan (- \frac{1}{3}))

sin (arcsin (\frac{5}{13}) + arcsin (\frac{4}{5}))