What is the general solution for solvefor x,sin(x)=-sqrt(2)*cos(x) ?

The general solution for solvefor x,sin(x)=-sqrt(2)*cos(x) is x=-0.95531…+pin

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solvefor x,sin(x)=-sqrt(2)*cos(x)

solve for

x, sin (x) = - 2 \cdot cos (x)

x = - 0.95531 \dots + πn

Degrees

x = - 54.73561 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (x) = - 2 cos (x)

Rewrite using trig identities

sin (x) = - 2 cos (x)

Divide both sides by

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

\frac{sin ( x )}{cos ( x )} = \frac{- 2 cos ( x )}{cos ( x )}

Simplify

\frac{sin ( x )}{cos ( x )} = - 2

Use the basic trigonometric identity:

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

tan (x) = - 2

tan (x) = - 2

Apply trig inverse properties

tan (x) = - 2

General solutions for

tan (x) = - 2

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

x = arctan (- 2) + πn

x = arctan (- 2) + πn

Show solutions in decimal form

x = - 0.95531 \dots + πn

cos (x) = \frac{1}{cos ^{2} ( x )}

2 cos (t) - 1 = 0, 0 <, = t \leq 2 π

2 sin (2 (θ + \frac{π}{6})) = - 2

tan (x) = 0.2092

sin (θ + 1) = cos (θ)

What is the general solution for solvefor x,sin(x)=-sqrt(2)*cos(x) ?
The general solution for solvefor x,sin(x)=-sqrt(2)*cos(x) is x=-0.95531…+pin