What is the value of ((3pi)/2)cos(0)-sec(2pi) ?

The value of ((3pi)/2)cos(0)-sec(2pi) is (3pi)/2-1

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((3pi)/2)cos(0)-sec(2pi)

(\frac{3 π}{2}) cos (0) - sec (2 π)

\frac{3 π}{2} - 1

Decimal Notation

3.71238 \dots

Solution steps

(\frac{3 π}{2}) cos (0) - sec (2 π)

= \frac{3 π}{2} cos (0) - sec (2 π)

Use the following trivial identity:

cos (0) = 1

cos (0)

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} 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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

Rewrite using trig identities:

sec (2 π) = 1

sec (2 π)

sec (2 π) = sec (0)

sec (2 π)

Rewrite

2 π

2 π + 0

= sec (2 π + 0)

Apply the periodicity of

sec

sec (x + 2 π) = sec (x)

sec (2 π + 0) = sec (0)

= sec (0)

= sec (0)

Use the following trivial identity:

sec (0) = 1

sec (0)

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}

= 1

= 1

= \frac{3 π}{2} \cdot 1 - 1

Simplify

= \frac{3 π}{2} - 1

sin^{3} (\frac{3 π}{4})

csc (- 1 4^{\circ})

- 1 sin (3 0^{\circ})

cot (12 9^{\circ})

18 sin (4 5^{\circ})

What is the value of ((3pi)/2)cos(0)-sec(2pi) ?
The value of ((3pi)/2)cos(0)-sec(2pi) is (3pi)/2-1