What is the value of csc(pi/3)-cos(pi/4) ?

The value of csc(pi/3)-cos(pi/4) is (2sqrt(3))/3-(sqrt(2))/2

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csc(pi/3)-cos(pi/4)

csc (\frac{π}{3}) - cos (\frac{π}{4})

\frac{2 3}{3} - \frac{2}{2}

Decimal Notation

0.44759 \dots

Solution steps

csc (\frac{π}{3}) - cos (\frac{π}{4})

Use the following trivial identity:

csc (\frac{π}{3}) = \frac{2 3}{3}

csc (\frac{π}{3})

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= \frac{2 3}{3}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

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}

= \frac{2}{2}

= \frac{2 3}{3} - \frac{2}{2}

sin^{2} (9)

cot (arcsin (0.8))

25 cos (3 5^{\circ})

\frac{tan ( 5 0 ^{\circ} ) - tan ( 4 0 ^{\circ} )}{tan ( 1 0 ^{\circ} )}

\frac{1}{arctan ( 0 )}

What is the value of csc(pi/3)-cos(pi/4) ?
The value of csc(pi/3)-cos(pi/4) is (2sqrt(3))/3-(sqrt(2))/2