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}

Solution steps

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

Rewrite using trig identities

tan (2.5 x) = 2.75

Apply trig inverse properties

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}

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)