What is the general solution for sin(x)+cos(x)=0,0<= x<= 360 ?

The general solution for sin(x)+cos(x)=0,0<= x<= 360 is x=135,x=315

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sin(x)+cos(x)=0,0<= x<= 360

sin (x) + cos (x) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

x = 13 5^{\circ}, x = 31 5^{\circ}

Radians

x = \frac{3 π}{4}, x = \frac{7 π}{4}

Solution steps

sin (x) + cos (x) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

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

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

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

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

Solutions for the range

0 \leq x \leq 36 0^{\circ}

x = 13 5^{\circ}, x = 31 5^{\circ}

sin (θ) = - 0.342

sin (x) = - 0.135

1 - csc^{2} (x) = cot^{2} (x)

sin (a) = 0.527

2 + 2 sin (θ) = 7 sin (θ)

What is the general solution for sin(x)+cos(x)=0,0<= x<= 360 ?
The general solution for sin(x)+cos(x)=0,0<= x<= 360 is x=135,x=315