1. Discuss the differences between the measurement of the surface area and the measurement of the volume of a right rectangular
2 answers:
For this case we have a rectangular prism.
The area is given by:
The volume is given by:
Where,
w: width
h: height
l: length
Part A:
The regions that are measured when we calculate the area are all the faces of the rectangular prism.
The regions that are measured when we calculate the volume are all the dimensions of the rectangular prism.
Part B:
Area: units ^ 2
Volume: units ^ 3
Part C:
Area: We want to calculate the amount of paint needed to paint a wooden box on the outside.
Volume: We want to calculate the amount of water inside a rectangular tank
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Answer:
- sin θ ≈ -0.08667
- cos θ ≈ 0.99624
Step-by-step explanation:
Straightforward use of the inverse tangent function of a calculator will tell you θ ≈ -0.08678 radians. This is an angle in the 4th quadrant, where your restriction on θ places it. (To comply with the restriction, you would need to consider the angle value to be 2π-0.08678 radians. The trig values for this angle are the same as the trig values for -0.08678 radians.)
Likewise, straightforward use of the calculator to find the other function values gives ...
sin(-0.08678 radians) ≈ -0.08667
cos(-0.08678 radians) ≈ 0.99624
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<em>Note on inverse tangent</em>
Depending on the mode setting of your calculator, the arctan or tan⁻¹ function may give you a value in degrees, not radians. That doesn't matter for this problem. sin(arctan(-0.087)) is the same whether the angle is degrees or radians, as long as you don't change the mode in the middle of the computation.
We have shown radians in the above answer because the restriction on the angle is written in terms of radians.
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<em>Alternate solution</em>
The relationship between tan and sin and cos in the 4th quadrant is ...
That is, the cosine is positive, and the sign of the sine matches that of the tangent.
This more complicated computation gives the same result as above.