What is the general solution for solvefor x,sin(x)+cos(x)=0 ?

The general solution for solvefor x,sin(x)+cos(x)=0 is x=(3pi)/4+pin

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solvefor x,sin(x)+cos(x)=0

solve for

x, sin (x) + cos (x) = 0

x = \frac{3 π}{4} + πn

Degrees

x = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

sin (x) + cos (x) = 0

Rewrite using trig identities

sin (x) + cos (x) = 0

Divide both sides by

cos (x), cos (x) \neq = 0

\frac{sin ( x ) + cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

\frac{sin ( x )}{cos ( x )} + 1 = 0

Use the basic trigonometric identity:

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

tan (x) + 1 = 0

tan (x) + 1 = 0

Move

1

to the right side

tan (x) + 1 = 0

Subtract

1

from both sides

tan (x) + 1 - 1 = 0 - 1

Simplify

tan (x) = - 1

tan (x) = - 1

General solutions for

tan (x) = - 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}

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

6 sin (x) = 3

4 csc (x) + 5 = 0

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

tan (x) + 1 = 0, 0 \leq x \leq 2 π

8 sin^{2} (θ) + 10 sin (θ) - 2 = 4 sin (θ) - 3

What is the general solution for solvefor x,sin(x)+cos(x)=0 ?
The general solution for solvefor x,sin(x)+cos(x)=0 is x=(3pi)/4+pin