Find tan0 if sin0= -1 and 0<0<2pie radians
If your question mean:
Find tan θ if sin θ = -1 and 0 < θ < 2 π radians
then
sin θ = - 1
for
θ = 3 π / 2 rad (270°)
cos θ = cos 3 π / 2
cos θ = 0
tan θ = sin θ / cos θ = -1 / 0 = undefined
To find the value of tan(0) given that sin(0)=-1, we can use the relationship between the trigonometric functions. In particular, we know that tan(0) is equal to sin(0) divided by cos(0).
However, we do not have information about cos(0) directly. But since 0 lies in the interval (0, 2π) radians, we can make use of the fact that sin(0) is negative to determine the quadrant in which 0 lies.
In the given interval, sin(0) is negative, which means that 0 lies in the third quadrant, where sin is negative and cos is positive.
In the third quadrant, cos(0) is positive, which implies that cos(0) > 0.
Now, let's use the relationship between sin(0), cos(0), and tan(0) to solve for tan(0):
tan(0) = sin(0) / cos(0)
Since sin(0) = -1 and cos(0) > 0, we have:
tan(0) = -1 / cos(0)
As cos(0) is positive and greater than 0, we can further simplify:
tan(0) = -1 / cos(0)
Therefore, the value of tan(0) is -1 divided by the value of cos(0), but without further information about cos(0), we cannot determine the exact value of tan(0).