The tanθ for the angle θ that lies in Quadrant III is √35
Trigonometry simply means the branch of mathematics that is concerned with functions of angles as well as their applications to calculation. It also deals with the relationship between ratios and their angles.
Given: The angle θ lies in Quadrant III
cosθ= −1/6 (adjacent/hypotenuse)
adjacent = -1 and hypotenuse = 6
We can draw the position of the angle as shown in the image attached.
Using Pythagoras' theorem:
opposite = √6²-(-1)² = √35
tanθ = (-√35) / (-1) = √35 (tanθ = opposite/adjacent)
Note: opposite in Quadrant III is negative
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