What is the general solution for cos(pi/4 c)=sin(2(pi/4)) ?

The general solution for cos(pi/4 c)=sin(2(pi/4)) is c=8n

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cos(pi/4 c)=sin(2(pi/4))

cos (\frac{π}{4} c) = sin (2 (\frac{π}{4}))

c = 8 n

Degrees

c = 0^{\circ} + 458.36623 \dots^{\circ} n

Solution steps

cos (\frac{π}{4} c) = sin (2 (\frac{π}{4}))

sin (2 \cdot \frac{π}{4}) = 1

sin (2 \cdot \frac{π}{4})

Simplify:

2 \cdot \frac{π}{4} = \frac{π}{2}

2 \cdot \frac{π}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 2}{4}

Cancel the common factor:

2

= \frac{π}{2}

= sin (\frac{π}{2})

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

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

= 1

= 1

cos (\frac{π}{4} c) = 1

General solutions for

cos (\frac{π}{4} c) = 1

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{π}{4} c = 0 + 2 πn

\frac{π}{4} c = 0 + 2 πn

Solve

\frac{π}{4} c = 0 + 2 πn : c = 8 n

\frac{π}{4} c = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{π}{4} c = 2 πn

Multiply both sides by

4

\frac{π}{4} c = 2 πn

Multiply both sides by

4

4 \cdot \frac{π}{4} c = 4 \cdot 2 πn

Simplify

π c = 8 πn

π c = 8 πn

Divide both sides by

π

π c = 8 πn

Divide both sides by

π

\frac{π c}{π} = \frac{8 πn}{π}

Simplify

c = 8 n

c = 8 n

c = 8 n

\frac{( 1 - tanh ( 2 x ) )}{( 1 + tanh ( 2 x ) )} = 2

sin (4 θ) = 0.345

- 3 = cot^{2} (x) + 3 csc (x)

4 cos^{2} (θ) + 3 cos (θ) = 1

arctan (\frac{1}{x}) + arctan (x) = \frac{π}{2}

What is the general solution for cos(pi/4 c)=sin(2(pi/4)) ?
The general solution for cos(pi/4 c)=sin(2(pi/4)) is c=8n