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2 answers:
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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.
Answer:
The dimension of the cardboard is 34 cm by 34 cm by 17 cm.
Step-by-step explanation:
Let the dimension of the cardboard box be x cm by y cm by z cm.
The surface area of the cardboard box without lid is
f(x,y,z)= xy+2xz+2yz.....(1)
Given that the volume of the cardboard is 19,652 cm³.
Therefore xyz =19,652
......(2)
putting the value of z in the equation (1)
The partial derivatives are
To find the dimension of the box set the partial derivatives and
.Therefore
.......(3)
and
.......(4)
Now putting the x in equation (3)
⇒y=34 cm
Then =34 cm.
Putting the value of x and y in the equation (2)
=17 cm.
The dimension of the cardboard is 34 cm by 34 cm by 17 cm.