if 0 is smaller then or equal to a which is < then 2pi then the equation sina=cos a has how many solutions? what are they? justify.
You will observe that there are two points at which the cross, and the
x's for these points are the values for which sin(x)=cos(x) and so are
the values of a that you require.
can be rearranged to tan(a)=1, so one solution is 45 degrees (pi/4 radian)
The other solution is in the third quadrant (where tan is positive) and so
is 180+45 degrees (pi+pi/4 radian)
if 0 < θ < 2π, then the equation sinθ = cosθ has how many solutions?
What are they? .Justify.
Divide both sides by cosθ, and we have: .tanθ .= .1
The only angles on the inteval [0, 2π) with a tangent of 1 are: .π/4 and 5π/4
Therefore, there are two solutions: .θ .= .π/4, 5π/4