Solve the equation 2 tan C - 3 = 3 tan C-4 algebraically for all values of C in the interval 0 degrees <_ C < 360 degrees
2tanC - 3 = 3tanC - 4,
3tanC - 2tanC = 4 - 3,
tanC = 1.0,
C = 45 Deg.
C = 45, and 225 Deg.
4 cos theta - 1
To solve the equation 2 tan C - 3 = 3 tan C - 4 algebraically for all values of C in the interval 0 degrees ≤ C < 360 degrees, follow these steps:
Step 1: Start by gathering all terms involving tangent functions on one side of the equation and constant terms on the other side. Rearrange the equation as follows:
2 tan C - 3 = 3 tan C - 4
Rearranging the equation gives:
2 tan C - 3 tan C = -4 + 3
Simplifying:
-tan C = -1
Step 2: To isolate the tangent function, multiply the equation by -1:
tan C = 1
Step 3: Now, we find the values of C that satisfy tan C = 1. Remember that tangent is positive in the first and third quadrants.
In the first quadrant (0 degrees < C < 90 degrees), we know that tan C = 1 when C = 45 degrees.
In the third quadrant (180 degrees < C < 270 degrees), tan C = 1 when C = 225 degrees.
Therefore, the solutions to the equation 2 tan C - 3 = 3 tan C - 4 in the interval 0 degrees ≤ C < 360 degrees are C = 45 degrees and C = 225 degrees.