What is the general solution for csc(t)= 1/(-(sqrt(2))/2) ?

The general solution for csc(t)= 1/(-(sqrt(2))/2) is t=(5pi)/4+2pin,t=(7pi)/4+2pin

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csc(t)= 1/(-(sqrt(2))/2)

csc (t) = \frac{1}{- \frac{2}{2}}

t = \frac{5 π}{4} + 2 πn, t = \frac{7 π}{4} + 2 πn

Solution steps

csc (t) = \frac{1}{- \frac{2}{2}}

Simplify

\frac{1}{- \frac{2}{2}} : - 2

\frac{1}{- \frac{2}{2}}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{1}{\frac{2}{2}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

\frac{1}{\frac{2}{2}} = \frac{2}{2}

= - \frac{2}{2}

Apply radical rule:

2 = 2^{\frac{1}{2}}

= \frac{2}{2 ^{\frac{1}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{2 ^{1}}{2 ^{\frac{1}{2}}} = 2^{1 - \frac{1}{2}}

= 2^{1 - \frac{1}{2}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= 2^{\frac{1}{2}}

Apply radical rule:

2^{\frac{1}{2}} = 2

= - 2

General solutions for

csc (t) = - 2

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

t = \frac{5 π}{4} + 2 πn, t = \frac{7 π}{4} + 2 πn

t = \frac{5 π}{4} + 2 πn, t = \frac{7 π}{4} + 2 πn

cos^{2} (x) = 1 - sin (x), 0 \leq x < 2 π

cos (2 x) - 3 sin (x) = 2, 0^{\circ} \leq x \leq 36 0^{\circ}

2 cos^{2} (x) + 3 cos (x) = 4 cos (x) + 1

6 sin^{2} (x) + 5 sin (x) = 0

sin (x) = - \frac{1}{2}, (0, 2 π)

What is the general solution for csc(t)= 1/(-(sqrt(2))/2) ?
The general solution for csc(t)= 1/(-(sqrt(2))/2) is t=(5pi)/4+2pin,t=(7pi)/4+2pin