What is the general solution for 4sin(t)-3cos(t)=0 ?

The general solution for 4sin(t)-3cos(t)=0 is t=0.64350…+pin

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4sin(t)-3cos(t)=0

4 sin (t) - 3 cos (t) = 0

t = 0.64350 \dots + πn

Degrees

t = 36.86989 \dots^{\circ} + 18 0^{\circ} n

Solution steps

4 sin (t) - 3 cos (t) = 0

Rewrite using trig identities

4 sin (t) - 3 cos (t) = 0

Divide both sides by

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

\frac{4 sin ( t ) - 3 cos ( t )}{cos ( t )} = \frac{0}{cos ( t )}

Simplify

\frac{4 sin ( t )}{cos ( t )} - 3 = 0

Use the basic trigonometric identity:

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

4 tan (t) - 3 = 0

4 tan (t) - 3 = 0

Move

3

to the right side

4 tan (t) - 3 = 0

Add

3

to both sides

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

Simplify

4 tan (t) = 3

4 tan (t) = 3

Divide both sides by

4

4 tan (t) = 3

Divide both sides by

4

\frac{4 tan ( t )}{4} = \frac{3}{4}

Simplify

tan (t) = \frac{3}{4}

tan (t) = \frac{3}{4}

Apply trig inverse properties

tan (t) = \frac{3}{4}

General solutions for

tan (t) = \frac{3}{4}

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

t = arctan (\frac{3}{4}) + πn

t = arctan (\frac{3}{4}) + πn

Show solutions in decimal form

t = 0.64350 \dots + πn

2 - 3 sin (θ) = cos (θ)

5 sin (3 x) = 4

sec (θ) = \frac{1}{cos ( 67.3 8 ^{\circ} )}

x, 6 cos^{2} (x) + cos (x) - 1 = 0

3 = tan (\frac{θ}{3})

What is the general solution for 4sin(t)-3cos(t)=0 ?
The general solution for 4sin(t)-3cos(t)=0 is t=0.64350…+pin