Answer:
θ = 5π/6 rad and 11π/6 rad
Step-by-step explanation:
Given the expression cotθ+√3=0
Subtract √3 from both sides
cotθ+√3-√3=0-√3
cotθ = -√3
Since cotθ = 1/tanθ
1/tanθ = -√3
Reciprocate both sides:
tanθ = -1/√3
θ = tan^-1(-1/√3)
θ = -30°
Since the angle is negative, and tanθ is negative in the second and fourth quadrant.
In the second quadrant;
θ = 180-30
θ = 150°
Since 180° = πrad
150° = 150π/180
150° = 5π/6 rad
In the fourth quadrant;
θ = 360-30
θ = 330°
Since 180° = πrad
330° = 330π/180
330° = 11π/6 rad
Hence the solutions are 5π/6 rad and 11π/6 rad.
Answer:
Step-by-step explanation:
Break down the figure into two shapes.
SHAPE A: The larger one. We can infer the size of the bottom is 6 cm because it's the same size as it's top counterpart. Same goes for the left side, which will have a measure of 7 cm.
SHAPE B: The smaller one. We're going to use the same method as we did with the first one, and infer the lengths of the other sides using the existing ones.
To calculate area, it's length times width.
SHAPE A: Its two side measures are 6 and 7, which equates to 42 cm^2.
SHAPE B: Its two side measures are 2 and 3, which equates to 6 cm^2.
If you add the two, the total area is 44 cm^2.
The area of a rectangle is easy to compute.
Area = length times height
Area = 8 cm * 4 cm = 32 square centimeters
