What is the general solution for 2sin(t)+3cos(t)=0 ?

The general solution for 2sin(t)+3cos(t)=0 is t=-0.98279…+pin

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

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

t = - 0.98279 \dots + πn

Degrees

t = - 56.30993 \dots^{\circ} + 18 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

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

\frac{2 sin ( t ) + 3 cos ( t )}{cos ( t )} = \frac{0}{cos ( t )}

Simplify

\frac{2 sin ( t )}{cos ( t )} + 3 = 0

Use the basic trigonometric identity:

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

2 tan (t) + 3 = 0

2 tan (t) + 3 = 0

Move

3

to the right side

2 tan (t) + 3 = 0

Subtract

3

from both sides

2 tan (t) + 3 - 3 = 0 - 3

Simplify

2 tan (t) = - 3

2 tan (t) = - 3

Divide both sides by

2

2 tan (t) = - 3

Divide both sides by

2

\frac{2 tan ( t )}{2} = \frac{- 3}{2}

Simplify

tan (t) = - \frac{3}{2}

tan (t) = - \frac{3}{2}

Apply trig inverse properties

tan (t) = - \frac{3}{2}

General solutions for

tan (t) = - \frac{3}{2}

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

t = arctan (- \frac{3}{2}) + πn

t = arctan (- \frac{3}{2}) + πn

Show solutions in decimal form

t = - 0.98279 \dots + πn

tan (θ) = \frac{- \frac{11}{3} - ( - \frac{4}{3} )}{1 + ( - \frac{4}{3} ) ( - \frac{11}{3} )}

csc (2 x) = 2, x 0^{\circ} < x < 36 0^{\circ}

tan (x) = \frac{6}{7}

4 sin^{2} (x) + 2 cos (x) = 3

10 cos (x) = 2.5 sin (x)

What is the general solution for 2sin(t)+3cos(t)=0 ?
The general solution for 2sin(t)+3cos(t)=0 is t=-0.98279…+pin