What is the general solution for sin(2.5x)=2.75cos(2.5x) ?

The general solution for sin(2.5x)=2.75cos(2.5x) is x=(1.22202…)/(2.5)+(pin)/(2.5)

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sin(2.5x)=2.75cos(2.5x)

sin (2.5 x) = 2.75 cos (2.5 x)

x = \frac{1.22202 \dots}{2.5} + \frac{πn}{2.5}

Degrees

x = 28.00675 \dots^{\circ} + 7 2^{\circ} n

Solution steps

sin (2.5 x) = 2.75 cos (2.5 x)

Rewrite using trig identities

sin (2.5 x) = 2.75 cos (2.5 x)

Divide both sides by

cos (2.5 x), cos (2.5 x) \neq = 0

\frac{sin ( 2.5 x )}{cos ( 2.5 x )} = \frac{2.75 cos ( 2.5 x )}{cos ( 2.5 x )}

Simplify

\frac{sin ( 2.5 x )}{cos ( 2.5 x )} = 2.75

Use the basic trigonometric identity:

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

tan (2.5 x) = 2.75

tan (2.5 x) = 2.75

Apply trig inverse properties

tan (2.5 x) = 2.75

General solutions for

tan (2.5 x) = 2.75

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

2.5 x = arctan (2.75) + πn

2.5 x = arctan (2.75) + πn

Solve

2.5 x = arctan (2.75) + πn : x = \frac{arctan ( 2.75 )}{2.5} + \frac{πn}{2.5}

2.5 x = arctan (2.75) + πn

Divide both sides by

2.5

2.5 x = arctan (2.75) + πn

Divide both sides by

2.5

\frac{2.5 x}{2.5} = \frac{arctan ( 2.75 )}{2.5} + \frac{πn}{2.5}

Simplify

x = \frac{arctan ( 2.75 )}{2.5} + \frac{πn}{2.5}

x = \frac{arctan ( 2.75 )}{2.5} + \frac{πn}{2.5}

x = \frac{arctan ( 2.75 )}{2.5} + \frac{πn}{2.5}

Show solutions in decimal form

x = \frac{1.22202 \dots}{2.5} + \frac{πn}{2.5}

cos (x) + 1 - 2 sin^{2} (x) = 0

- 3 = tan (x)

sin (2 w) = 0

4 sin^{(2)} (θ) - 3 = 0

3 cos (5 t) = 0

What is the general solution for sin(2.5x)=2.75cos(2.5x) ?
The general solution for sin(2.5x)=2.75cos(2.5x) is x=(1.22202…)/(2.5)+(pin)/(2.5)