What is the general solution for 5sin(x)=3,sin(x)+cos(x) ?

The general solution for 5sin(x)=3,sin(x)+cos(x) is No Solution for x\in\mathbb{R}

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5sin(x)=3,sin(x)+cos(x)

5 sin (x) = 3, sin (x) + cos (x)

No Solution for x \in R

Solution steps

5 sin (x) = 3, sin (x) + cos (x)

Divide both sides by

5

5 sin (x) = 3

Divide both sides by

5

\frac{5 sin ( x )}{5} = \frac{3}{5}

Simplify

sin (x) = \frac{3}{5}

sin (x) = \frac{3}{5}

Apply trig inverse properties

sin (x) = \frac{3}{5}

General solutions for

sin (x) = \frac{3}{5}

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

x = arcsin (\frac{3}{5}) + 2 πn, x = π - arcsin (\frac{3}{5}) + 2 πn

x = arcsin (\frac{3}{5}) + 2 πn, x = π - arcsin (\frac{3}{5}) + 2 πn

Solutions for the range

sin (x) + cos (x)

No Solution for x \in R

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

20 sin (t) cos (t) = - 4 sin (t)

cos (x) - cos (2 x) = 0, 0^{\circ} \leq x < 36 0^{\circ}

3 = - 3 cos (θ)

2 cos (θ) - 3 = 0, 0 \leq θ \leq 2 π

What is the general solution for 5sin(x)=3,sin(x)+cos(x) ?
The general solution for 5sin(x)=3,sin(x)+cos(x) is No Solution for x\in\mathbb{R}