What is the general solution for sin(3*x)=cos(x) ?

The general solution for sin(3*x)=cos(x) is x=(pi+4pin)/8 ,x=(pi+4pin)/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(3*x)=cos(x)

sin (3 \cdot x) = cos (x)

x = \frac{π + 4 πn}{8}, x = \frac{π + 4 πn}{4}

Solution steps

sin (3 x) = cos (x)

Rewrite using trig identities

sin (3 x) = sin (\frac{π}{2} - x)

Apply trig inverse properties

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

3 x = \frac{π}{2} - x + 2 πn : x = \frac{π + 4 πn}{8}

3 x = π - (\frac{π}{2} - x) + 2 πn : x = \frac{π + 4 πn}{4}

x = \frac{π + 4 πn}{8}, x = \frac{π + 4 πn}{4}

sin^{22} (x) = sin^{2} (x)

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

cos (8 t) - 5 sin (8 t) = 0

cos^{2} (x) + 3 sin (x) + 1 = 0

\frac{a ^{0.2}}{( cos ^{2} ( x ) ) - cos ^{2} ( x ) - 1} = 0

What is the general solution for sin(3*x)=cos(x) ?
The general solution for sin(3*x)=cos(x) is x=(pi+4pin)/8 ,x=(pi+4pin)/4