Question

simplify: 4sin tetha - 3cos tetha=0​

Answer 1

Answer:

answer is 3 sin theta - 4 cos theta

Answer 2

Answer:

4sin2(θ)=3cos2(θ), 0<θ<360◦

Subtract 3cos2(θ) from both sides

4sin2(θ)−3cos2(θ)=0

Show Steps

Factor 4sin2(θ)−3cos2(θ): (2sin(θ)+√3cos(θ))(2sin(θ)−√3cos(θ))

(2sin(θ)+√3cos(θ))(2sin(θ)−√3cos(θ))=0

Solving each part separately

2sin(θ)+√3cos(θ)=0 or 2sin(θ)−√3cos(θ)=0

Show Steps

2sin(θ)+√3cos(θ)=0, 0<θ<360◦ : θ=−arctan(

√3

2 )+180◦ , θ=−arctan(

√3

2 )+360◦

Show Steps

2sin(θ)−√3cos(θ)=0, 0<θ<360◦ : θ=arctan(

√3

2 ), θ=arctan(

√3

2 )+180◦

Combine all the solutions

θ=−arctan(

√3

2 )+180◦ , θ=−arctan(

√3

2 )+360◦ , θ=arctan(

√3

2 ), θ=arctan(

√3

2 )+180◦

Show solutions in decimal form

θ=−0.71372…+180◦ , θ=−0.71372…+360◦ , θ=0.71372…, θ=0.71372…+180◦