en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(4+tan(x))(3sin(x)-2)=0

Solution

(4 + tan (x)) (3 sin (x) - 2) = 0

Solution

x = - 1.32581 \dots + πn, x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn

+1

Degrees

x = - 75.96375 \dots^{\circ} + 18 0^{\circ} n, x = 41.81031 \dots^{\circ} + 36 0^{\circ} n, x = 138.18968 \dots^{\circ} + 36 0^{\circ} n

Solution steps

(4 + tan (x)) (3 sin (x) - 2) = 0

Solving each part separately

4 + tan (x) = 0 or 3 sin (x) - 2 = 0

4 + tan (x) = 0 : x = arctan (- 4) + πn

4 + tan (x) = 0

Move

4

to the right side

4 + tan (x) = 0

Subtract

4

from both sides

4 + tan (x) - 4 = 0 - 4

Simplify

tan (x) = - 4

tan (x) = - 4

Apply trig inverse properties

tan (x) = - 4

General solutions for

tan (x) = - 4

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

x = arctan (- 4) + πn

x = arctan (- 4) + πn

3 sin (x) - 2 = 0 : x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

3 sin (x) - 2 = 0

Move

2

to the right side

3 sin (x) - 2 = 0

Add

2

to both sides

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

Simplify

3 sin (x) = 2

3 sin (x) = 2

Divide both sides by

3

3 sin (x) = 2

Divide both sides by

3

\frac{3 sin ( x )}{3} = \frac{2}{3}

Simplify

sin (x) = \frac{2}{3}

sin (x) = \frac{2}{3}

Apply trig inverse properties

sin (x) = \frac{2}{3}

General solutions for

sin (x) = \frac{2}{3}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

Combine all the solutions

x = arctan (- 4) + πn, x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

Show solutions in decimal form

x = - 1.32581 \dots + πn, x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn

Popular Examples

sec (2 x) - 1 = 0

sin(2x)+sin(x)+2cos(x)+1=0

sin (2 x) + sin (x) + 2 cos (x) + 1 = 0

csc (x) = \frac{13}{5}

6 csc (θ) + 7 = 0

cos(2x)+cos(x)=0,0<= x<= 2pi

cos (2 x) + cos (x) = 0, 0 \leq x \leq 2 π