Question

Solve sinθcosθ-cosθ=0 for 0≤θ<2π

Answer 1

I have done the following:

sinθcosθ-cosθ=0

Forming Factors

cosθ(sinθ-1)=0

Using Zero-Product Property

either cosθ=0 => θ=π/2

or sinθ-1=0 => sinθ=1 => θ=π/2


Any other values for the angles????

Answer 2

You are absolutely right mate.....

Answer 3

But book gives answer as π/2 and 3π/2

Answer 4

well cos 270=0 and sin 270=-1,,,, so all you have to see is how many values are there which give the solution.so the book is right. You were right as well but 90 is just one angle. You should memorize important angles because they really help.

Answer 5

because cos (3pi/2) = 0 also...

Answer 6

your firs factor of cos(theta) = 0 has two values of theta that makes that true.

Answer 7

but for the other factor there is only one value...right???

Answer 8

no as sin 270=-1 which makes sin(theta)+1=0

Answer 9

cos(3pi/2) = 0

Answer 10

\[\cos \theta = 0\]