What is the general solution for 3sin(x)=7cos(x) ?

The general solution for 3sin(x)=7cos(x) is x=1.16590…+pin

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3sin(x)=7cos(x)

3 sin (x) = 7 cos (x)

x = 1.16590 \dots + πn

Solution steps

3 sin (x) = 7 cos (x)

Rewrite using trig identities

3 tan (x) = 7

Divide both sides by

3

tan (x) = \frac{7}{3}

Apply trig inverse properties

x = arctan (\frac{7}{3}) + πn

Show solutions in decimal form

x = 1.16590 \dots + πn

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2 sin (x) - tan (x) = 0

2 sin^{2} (x) - 13 sin (x) + 6 = 0

What is the general solution for 3sin(x)=7cos(x) ?
The general solution for 3sin(x)=7cos(x) is x=1.16590…+pin