What is the general solution for sin(2t)=-cos(2t) ?

The general solution for sin(2t)=-cos(2t) is t=(3pi)/8+(pin)/2

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sin(2t)=-cos(2t)

sin (2 t) = - cos (2 t)

t = \frac{3 π}{8} + \frac{πn}{2}

Degrees

t = 67. 5^{\circ} + 9 0^{\circ} n

Solution steps

sin (2 t) = - cos (2 t)

Rewrite using trig identities

sin (2 t) = - cos (2 t)

Divide both sides by

cos (2 t), cos (2 t) \neq = 0

\frac{sin ( 2 t )}{cos ( 2 t )} = \frac{- cos ( 2 t )}{cos ( 2 t )}

Simplify

\frac{sin ( 2 t )}{cos ( 2 t )} = - 1

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

tan (2 t) = - 1

tan (2 t) = - 1

General solutions for

tan (2 t) = - 1

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

2 t = \frac{3 π}{4} + πn

2 t = \frac{3 π}{4} + πn

Solve

2 t = \frac{3 π}{4} + πn : t = \frac{3 π}{8} + \frac{πn}{2}

2 t = \frac{3 π}{4} + πn

Divide both sides by

2

2 t = \frac{3 π}{4} + πn

Divide both sides by

2

\frac{2 t}{2} = \frac{\frac{3 π}{4}}{2} + \frac{πn}{2}

Simplify

\frac{2 t}{2} = \frac{\frac{3 π}{4}}{2} + \frac{πn}{2}

Simplify

\frac{2 t}{2} : t

\frac{2 t}{2}

Divide the numbers:

\frac{2}{2} = 1

= t

Simplify

\frac{\frac{3 π}{4}}{2} + \frac{πn}{2} : \frac{3 π}{8} + \frac{πn}{2}

\frac{\frac{3 π}{4}}{2} + \frac{πn}{2}

\frac{\frac{3 π}{4}}{2} = \frac{3 π}{8}

\frac{\frac{3 π}{4}}{2}

Apply the fraction rule:

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

= \frac{3 π}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= \frac{3 π}{8}

= \frac{3 π}{8} + \frac{πn}{2}

t = \frac{3 π}{8} + \frac{πn}{2}

t = \frac{3 π}{8} + \frac{πn}{2}

t = \frac{3 π}{8} + \frac{πn}{2}

t = \frac{3 π}{8} + \frac{πn}{2}

cos (3 θ) = sin (3 θ)

cos (5 x) = 1, 0 \leq x \leq \frac{π}{2}

sec (x) = - 1 + tan (x)

cos (2 x) + 2 cos^{2} (x) = 0

x, csc (x) + cot (x) = 1

What is the general solution for sin(2t)=-cos(2t) ?
The general solution for sin(2t)=-cos(2t) is t=(3pi)/8+(pin)/2