What is the general solution for 7cos(x)-7sin(x)=0 ?

The general solution for 7cos(x)-7sin(x)=0 is x= pi/4+pin

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7cos(x)-7sin(x)=0

7 cos (x) - 7 sin (x) = 0

x = \frac{π}{4} + πn

Degrees

x = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

7 cos (x) - 7 sin (x) = 0

Rewrite using trig identities

7 cos (x) - 7 sin (x) = 0

Divide both sides by

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

\frac{7 cos ( x ) - 7 sin ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

7 - \frac{7 sin ( x )}{cos ( x )} = 0

Use the basic trigonometric identity:

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

7 - 7 tan (x) = 0

7 - 7 tan (x) = 0

Move

7

to the right side

7 - 7 tan (x) = 0

Subtract

7

from both sides

7 - 7 tan (x) - 7 = 0 - 7

Simplify

- 7 tan (x) = - 7

- 7 tan (x) = - 7

Divide both sides by

- 7

- 7 tan (x) = - 7

Divide both sides by

- 7

\frac{- 7 tan ( x )}{- 7} = \frac{- 7}{- 7}

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

9 sin (x) cos (x) = 5 cos (x)

3 cos (x) sin (x) = - sin (x)

4 cos (10 x) + 2 = 2

sin (x) = - \frac{3}{4}

sin (2 x - \frac{π}{3}) = \frac{1}{2}

What is the general solution for 7cos(x)-7sin(x)=0 ?
The general solution for 7cos(x)-7sin(x)=0 is x= pi/4+pin