To find the value of the expression sin(6π/5) * tan(7π/3), we first need to calculate the values of sin(6π/5) and tan(7π/3).
sin(6π/5): Using the unit circle, we can see that 6π/5 is in the second quadrant, where sine is positive. Thus, sin(6π/5) = sin(π - π/5) = sin(π/5) = √(1 - cos^2(π/5)). We can then use the cosine half-angle identity to calculate cos(π/5) and determine the value of sin(6π/5).
tan(7π/3): Using the unit circle, we can see that 7π/3 is in the third quadrant, where tangent is negative. To find the value of tan(7π/3), we should first calculate sin(7π/3) and cos(7π/3) and then divide sin(7π/3) by cos(7π/3) to get tan(7π/3).
Once we have the values of sin(6π/5) and tan(7π/3), we can multiply them together to get the final result.
To find the value of the expression sin(6π/5) * tan(7π/3), we first need to calculate the values of sin(6π/5) and tan(7π/3).
sin(6π/5):
Using the unit circle, we can see that 6π/5 is in the second quadrant, where sine is positive. Thus, sin(6π/5) = sin(π - π/5) = sin(π/5) = √(1 - cos^2(π/5)). We can then use the cosine half-angle identity to calculate cos(π/5) and determine the value of sin(6π/5).
tan(7π/3):
Using the unit circle, we can see that 7π/3 is in the third quadrant, where tangent is negative. To find the value of tan(7π/3), we should first calculate sin(7π/3) and cos(7π/3) and then divide sin(7π/3) by cos(7π/3) to get tan(7π/3).
Once we have the values of sin(6π/5) and tan(7π/3), we can multiply them together to get the final result.