Given that TanA= -0.5774, find A if 360°<A<540°
We know that TanA = opposite/adjacent, so we can set up a right triangle where A is an angle in the second quadrant (since Tan is negative) and label the opposite side as x and the adjacent side as 1.
Using the Pythagorean theorem, we can solve for the hypotenuse:
h = sqrt(x^2 + 1^2)
Now we can use the given information that 360° < A < 540° to determine the reference angle for A:
reference angle = A - 360°
reference angle = 540° - A
Since the tangent function is negative in the second and fourth quadrants, we know that the reference angle is either 119.036° or 299.036°.
Now we can set up the equation:
TanA = -0.5774
Tan(reference angle) = -0.5774
And solve for the angle:
reference angle = arctan(-0.5774)
reference angle = -29.744°
Since we know that A is in the second quadrant, we add 180° to the reference angle to get:
A = 150.256°
Therefore, A = 150.256° satisfies the conditions of 360° < A < 540° and TanA = -0.5774.
To find the value of A within the given range, we can use inverse tangent (arctan) function on -0.5774.
Step 1: Calculate the arctan of -0.5774.
A = arctan(-0.5774)
Step 2: Convert the result to degrees.
A ≈ -30.96°
Since the given range is 360° < A < 540°, the value of A within this range is approximately -30.96°. However, angles are conventionally measured between 0° to 360° or 0° to 2π radians.