sin((7pi/6) - (pi/3))
= - sqrt3?
cannot be. |sin(x)| <= 1 for any x.
7pi/6 - pi/3 = 2pi/3
so, what is sin(2pi/3) = sin(pi/3) ?
sqrt3/2?
that's better
To find the value of sin((7π/6) - (π/3)), we can follow these steps:
Step 1: Simplify the given expression: (7π/6) - (π/3)
To simplify, we need a common denominator for π/3 and 7π/6. Their common denominator is 6.
(7π/6) - (π/3) = (7π - 2π) / 6
= 5π / 6
Step 2: Determine the reference angle
The reference angle is the positive acute angle between the terminal side and the x-axis. Since our angle, 5π/6, is in the second quadrant, we need to find the reference angle in the first quadrant. To do this, subtract 5π/6 from π to get the reference angle:
Reference angle = π - 5π/6
= (6π/6) - (5π/6)
= π/6
Step 3: Determine the sign of the value
Since sine is negative in the second quadrant, the value of sin(5π/6) would be negative.
Step 4: Find the value of sin(π/6)
In the first quadrant, the sine of π/6 is 1/2.
Step 5: Apply the sign from Step 3 to the value from Step 4
Since sin(5π/6) is negative, the value would be -1/2.
Therefore, sin((7π/6) - (π/3)) = -1/2.