Solve the given equation and indicate the number of values of θ sach that 0≤θ<2π ,that satisfy the iquation;
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Is the equation: sin(a) = sqrt(3)/2 ? There are 2 angles that have a positive (sin) of sqrt(3)/2 in the unit circle.
To solve the equation: we use the (sin inverse) functions; they take a number and spit back an angle.
sin(a) = sqrt(3)/2
sin-1(sin(a)) = sin-1(sqrt(3)/2)
a = sin-1(sqrt(3)/2)
a = pi/3
Now the issue here is that sin-1 only gives you an angle between (-pi/2) and (pi/2) so you have to revert back to the original question to ALL the angles.
60 degrees (pi/3) and,
120 degrees (2pi/3)
Does that make sense?
Equation is sina=plus,minus 1/2 sqrt(3)?
If it is sin(a) = +- sqrt(3)/2 then there are 4 angles that we can use; and they all have a reference angle of (60 degrees).
In quadrant 1 we have (pi/3) which is 60 degrees
In quadrant 2 we have (2pi/3) which is 120 degrees
In quadrant 3 we have (4pi/3) which is 240 degrees
In quadrant 4 we have (5pi/3) which is 320 degrees