What is the general solution for solvefor x,-44sin(2x)+42cos(2x)=0 ?

The general solution for solvefor x,-44sin(2x)+42cos(2x)=0 is x=(0.76214…)/2+(pin)/2

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solvefor x,-44sin(2x)+42cos(2x)=0

solve for

x, - 44 sin (2 x) + 42 cos (2 x) = 0

x = \frac{0.76214 \dots}{2} + \frac{πn}{2}

Solution steps

- 44 sin (2 x) + 42 cos (2 x) = 0

Rewrite using trig identities

- 44 tan (2 x) + 42 = 0

Move

42

to the right side

- 44 tan (2 x) = - 42

Divide both sides by

- 44

tan (2 x) = \frac{21}{22}

Apply trig inverse properties

2 x = arctan (\frac{21}{22}) + πn

Solve

2 x = arctan (\frac{21}{22}) + πn : x = \frac{arctan ( \frac{21}{22} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{21}{22} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{0.76214 \dots}{2} + \frac{πn}{2}

sin^{2} (x) - sin (x) = 1 - sin^{2} (x)

sin (x) = \frac{2 π}{3}

cos (3 x) + sin (2 x) + cos (x) = 0

tan (2 θ) = 1.333

- csc^{2} (x) = - \frac{4}{3}

What is the general solution for solvefor x,-44sin(2x)+42cos(2x)=0 ?
The general solution for solvefor x,-44sin(2x)+42cos(2x)=0 is x=(0.76214…)/2+(pin)/2