What is the general solution for (cos(x))(bsin(x)-a)=0,0<= x<2pi ?

The general solution for (cos(x))(bsin(x)-a)=0,0<= x<2pi is x= pi/2 ,x=(3pi)/2

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(cos(x))(bsin(x)-a)=0,0<= x<2pi

(cos (x)) (b sin (x) - a) = 0, 0 \leq x < 2 π

x = \frac{π}{2}, x = \frac{3 π}{2}

Degrees

x = 9 0^{\circ}, x = 27 0^{\circ}

Solution steps

(cos (x)) (b sin (x) - a) = 0, 0 \leq x < 2 π

Solving each part separately

cos (x) = 0 or b sin (x) - a = 0

cos (x) = 0, 0 \leq x < 2 π : x = \frac{π}{2}, x = \frac{3 π}{2}

cos (x) = 0, 0 \leq x < 2 π

General solutions for

cos (x) = 0

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

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

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

Solutions for the range

0 \leq x < 2 π

x = \frac{π}{2}, x = \frac{3 π}{2}

b sin (x) - a = 0, 0 \leq x < 2 π :

No Solution

b sin (x) - a = 0, 0 \leq x < 2 π

Move

a

to the right side

b sin (x) - a = 0

Add

a

to both sides

b sin (x) - a + a = 0 + a

Simplify

b sin (x) = a

b sin (x) = a

Divide both sides by

b; b \neq = 0

b sin (x) = a

Divide both sides by

b; b \neq = 0

\frac{b sin ( x )}{b} = \frac{a}{b}; b \neq = 0

Simplify

sin (x) = \frac{a}{b}; b \neq = 0

sin (x) = \frac{a}{b}; b \neq = 0

Apply trig inverse properties

sin (x) = \frac{a}{b}

General solutions for

sin (x) = \frac{a}{b}

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

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

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

Solutions for the range

0 \leq x < 2 π

No Solution

Combine all the solutions

x = \frac{π}{2}, x = \frac{3 π}{2}

cos (x) = - \frac{5}{34}

sin (3 x) = \frac{1}{2}, 0 \leq x \leq 1

sec (θ) = - \frac{1}{2}

cos (x) = cos (x - c)

4 cos (120 t) = 0

What is the general solution for (cos(x))(bsin(x)-a)=0,0<= x<2pi ?
The general solution for (cos(x))(bsin(x)-a)=0,0<= x<2pi is x= pi/2 ,x=(3pi)/2