What is the general solution for cos(x)-sin(x)=0,y(0)=3 ?

The general solution for cos(x)-sin(x)=0,y(0)=3 is No Solution for x\in\mathbb{R}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(x)-sin(x)=0,y(0)=3

cos (x) - sin (x) = 0, y (0) = 3

No Solution for x \in R

Solution steps

cos (x) - sin (x) = 0, y (0) = 3

Rewrite using trig identities

cos (x) - sin (x) = 0

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

1 - tan (x) = 0

1 - tan (x) = 0

Move

1

to the right side

1 - tan (x) = 0

Subtract

1

from both sides

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

Simplify

- tan (x) = - 1

- tan (x) = - 1

Divide both sides by

- 1

- tan (x) = - 1

Divide both sides by

- 1

\frac{- tan ( x )}{- 1} = \frac{- 1}{- 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{π}{4} + πn

x = \frac{π}{4} + πn

Solutions for the range

y (0) = 3

No Solution for x \in R

cos (x) + 3 sin (x) = 3

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

sec (x + 4 5^{\circ}) = 1

117.72 sin (θ) - 35.316 cos (θ) - 12.5 = 0

- 2 sin (θ) = 0

What is the general solution for cos(x)-sin(x)=0,y(0)=3 ?
The general solution for cos(x)-sin(x)=0,y(0)=3 is No Solution for x\in\mathbb{R}