What is the general solution for solvefor x,0.05cos(x)=-sin(x) ?

The general solution for solvefor x,0.05cos(x)=-sin(x) is x=-0.04995…+pin

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solvefor x,0.05cos(x)=-sin(x)

solve for

x, 0.05 cos (x) = - sin (x)

x = - 0.04995 \dots + πn

Degrees

x = - 2.86240 \dots^{\circ} + 18 0^{\circ} n

Solution steps

0.05 cos (x) = - sin (x)

Rewrite using trig identities

0.05 cos (x) = - sin (x)

Divide both sides by

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

\frac{0.05 cos ( x )}{cos ( x )} = \frac{- sin ( x )}{cos ( x )}

Simplify

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

Use the basic trigonometric identity:

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

0.05 = - tan (x)

Switch sides

- tan (x) = 0.05

- tan (x) = 0.05

Divide both sides by

- 1

- tan (x) = 0.05

Divide both sides by

- 1

\frac{- tan ( x )}{- 1} = \frac{0.05}{- 1}

Simplify

tan (x) = - 0.05

tan (x) = - 0.05

Apply trig inverse properties

tan (x) = - 0.05

General solutions for

tan (x) = - 0.05

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- 0.05) + πn

x = arctan (- 0.05) + πn

Show solutions in decimal form

x = - 0.04995 \dots + πn

cos (x^{\circ}) = \frac{20.26}{26.4473}

cos (x) = \frac{- \frac{4}{3} 3}{\frac{8}{3} 3}

cos (θ) = \frac{3}{10}

27 tan^{2} (x) - 9 = 0

tan (x) = \frac{8}{17}

What is the general solution for solvefor x,0.05cos(x)=-sin(x) ?
The general solution for solvefor x,0.05cos(x)=-sin(x) is x=-0.04995…+pin