"solve for the following trig ratios using the unit circle":
1 answer:
<h3>Answer: -1</h3>
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Explanation:
The goal is to get that 1755 degree angle between 0 and 360, so we can refer to the unit circle later.
Subtract off 360 from this until we get to that target
- 1755 - 360 = 1395
- 1395 - 360 = 1035
- 1035 - 360 = 675
- 675 - 360 = 315
Or a shortcut could be
- 1755 - 4*360 = 315
The angles of 1755 degrees and 315 degrees are coterminal. They point in the same exact direction which is directly southeast in quadrant IV.
Now use the unit circle (see below) to find that
- sin(315) = -sqrt(2)/2
- cos(315) = sqrt(2)/2
Dividing those two items and simplifying gets us
tan(315) = sin(315)/cos(315) = -1
Then we go from tan(315) = -1 to tan(1755) = -1
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Answer:
This is the same as writing 7*Ln( e^(2x) + 10) + C
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Explanation:
Start with the equation
Apply the derivative and multiply both sides by 7 like so
The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)
This way we can do the following substitutions:
Integrating leads to
Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.
To verify the answer, you can apply the derivative to it and you should get back to the original integrand of