Parameterize the surface (call it 
) by
with
and 
, which yields
Then the area of is given by the surface integral
with
Then the area of
Find the measure of the reference angle for each given angle. Part 2
2 answers:
Answer:
13. 20°
14. 15°
15. 50°
Step-by-step explanation:
Please see the attached pictures for full solution.
For negative angles, the arrow turns clockwise.
Answer:
13. 20°
14. 15°
15. 50°
Step-by-step explanation:
From a mathematical point of view, the reference angle is the smaller of α and (180°-α), where α = θ mod 180°.
That is, add or subtract multiples of 180° until the result is in the range 0–180°. Then choose the smaller of the angle and its supplement.
It is convenient to let a spreadsheet calculate these when you have a bunch of them.
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From a geometrical point of view, the reference angle is the positive angle between the terminal ray and the nearest x-axis.
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For the angles here, the reference angles (in degrees) are shown in the attachment.
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