What is the value of -cot(pi/4)+csc(pi/4) ?

The value of -cot(pi/4)+csc(pi/4) is -1+sqrt(2)

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-cot(pi/4)+csc(pi/4)

- cot (\frac{π}{4}) + csc (\frac{π}{4})

- 1 + 2

Decimal Notation

0.41421 \dots

Solution steps

- cot (\frac{π}{4}) + csc (\frac{π}{4})

Use the following trivial identity:

cot (\frac{π}{4}) = 1

cot (\frac{π}{4})

cot (x)

periodicity table with

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 1

Use the following trivial identity:

csc (\frac{π}{4}) = 2

csc (\frac{π}{4})

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

= 2

= - 1 + 2

arcsin (\frac{0}{5})

arcsin (0.385)

16 \cdot cos (4 5^{\circ})

\frac{9.8 sin ( 83. 5 ^{\circ} )}{12.3}

\frac{340 \cdot sin ( 1 5 ^{\circ} )}{sin ( 6 0 ^{\circ} )}

What is the value of -cot(pi/4)+csc(pi/4) ?
The value of -cot(pi/4)+csc(pi/4) is -1+sqrt(2)