First, we need to find the value of arctg(-1/3). The arctangent function returns an angle whose tangent is equal to -1/3. We need to find the angle in the fourth quadrant, where the tangent is negative.
Let's find the reference angle first:tan(theta) = -1/3theta = arctan(-1/3) = -0.32175 (approximately)
Since the tangent is negative in the fourth quadrant, we can find the angle:-0.32175 + 2π = 5.9616 (approximately)
Now we can calculate sin(arctg(-1/3) + 3π/2):sin(5.9616 + 3π/2) = sin(5.9616 + 4.7124) = sin(10.674) ≈ sin(2.069) ≈ 0.884
Therefore, sin(arctg(-1/3) + 3π/2) is approximately 0.884.
First, we need to find the value of arctg(-1/3). The arctangent function returns an angle whose tangent is equal to -1/3. We need to find the angle in the fourth quadrant, where the tangent is negative.
Let's find the reference angle first:
tan(theta) = -1/3
theta = arctan(-1/3) = -0.32175 (approximately)
Since the tangent is negative in the fourth quadrant, we can find the angle:
-0.32175 + 2π = 5.9616 (approximately)
Now we can calculate sin(arctg(-1/3) + 3π/2):
sin(5.9616 + 3π/2) = sin(5.9616 + 4.7124) = sin(10.674) ≈ sin(2.069) ≈ 0.884
Therefore, sin(arctg(-1/3) + 3π/2) is approximately 0.884.