What is the general solution for 6sin(x)-2cos(x)=7 ?

The general solution for 6sin(x)-2cos(x)=7 is No Solution for x\in\mathbb{R}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

6sin(x)-2cos(x)=7

6 sin (x) - 2 cos (x) = 7

No Solution for x \in R

Solution steps

6 sin (x) - 2 cos (x) = 7

Add

2 cos (x)

to both sides

6 sin (x) = 7 + 2 cos (x)

Square both sides

(6 sin (x))^{2} = (7 + 2 cos (x))^{2}

Subtract

(7 + 2 cos (x))^{2}

from both sides

36 sin^{2} (x) - 49 - 28 cos (x) - 4 cos^{2} (x) = 0

Rewrite using trig identities

- 13 - 28 cos (x) - 40 cos^{2} (x) = 0

Solve by substitution

cos (x) = - \frac{7}{20} - i \frac{9}{20}, cos (x) = - \frac{7}{20} + i \frac{9}{20}

cos (x) = - \frac{7}{20} - i \frac{9}{20} :

No Solution

cos (x) = - \frac{7}{20} + i \frac{9}{20} :

No Solution

Combine all the solutions

No Solution

Verify solutions by plugging them into the original equation

No Solution for x \in R

csc^{2} (x) + 4 csc (x) - 5 = 0

90 + 45 cos (\frac{t ^{2}}{18}) - 100 = 0

3 tan^{3} (x) + 3 tan^{2} (x) - tan (x) - 1 = 0

8 sin (x) = 4 cos^{2} (x) - 7

cos (x) - 1 = 0, 0 \leq x \leq 2 π

What is the general solution for 6sin(x)-2cos(x)=7 ?
The general solution for 6sin(x)-2cos(x)=7 is No Solution for x\in\mathbb{R}