What is the slope of the line that passes through points (1,7),(10,1)
2 answers:
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Let
because that is the range of the inverse cosine funcition.
Also,
![\mathsf{cos\,\theta=cos\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]}\\\\\\ \mathsf{cos\,\theta=\dfrac{4}{5}}\\\\\\ \mathsf{5\,cos\,\theta=4}](https://tex.z-dn.net/?f=%5Cmathsf%7Bcos%5C%2C%5Ctheta%3Dcos%5C%21%5Cleft%5Bcos%5E%7B-1%7D%5C%21%5Cleft%28%5Cdfrac%7B4%7D%7B5%7D%5Cright%29%5Cright%5D%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7Bcos%5C%2C%5Ctheta%3D%5Cdfrac%7B4%7D%7B5%7D%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7B5%5C%2Ccos%5C%2C%5Ctheta%3D4%7D)
Square both sides and apply the fundamental trigonometric identity:
But which means 
lies either in the 1st or the 2nd quadrant. So 
is a positive number:
![\mathsf{sin\,\theta=\dfrac{3}{5}}\\\\\\ \therefore~~\mathsf{sin\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]=\dfrac{3}{5}\qquad\quad\checkmark}](https://tex.z-dn.net/?f=%5Cmathsf%7Bsin%5C%2C%5Ctheta%3D%5Cdfrac%7B3%7D%7B5%7D%7D%5C%5C%5C%5C%5C%5C%0A%5Ctherefore~~%5Cmathsf%7Bsin%5C%21%5Cleft%5Bcos%5E%7B-1%7D%5C%21%5Cleft%28%5Cdfrac%7B4%7D%7B5%7D%5Cright%29%5Cright%5D%3D%5Cdfrac%7B3%7D%7B5%7D%5Cqquad%5Cquad%5Ccheckmark%7D)
I hope this helps. =)
Tags: <em>inverse trigonometric function cosine sine cos sin trig trigonometry</em>
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Let
Also,
Square both sides and apply the fundamental trigonometric identity:
But
I hope this helps. =)
Tags: <em>inverse trigonometric function cosine sine cos sin trig trigonometry</em>
The earth is 40000 kilometers around. There is no need to round off because the circumference already contains significant figures.
How do I calculate a circle's circumference?
A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14).
Given: theta angle (central) = 7.2°; arc length S = 800 km
This indicates that an 800 km long arc is extending a circle with a 7.2° center angle ( earth in this case).
By definition, "An arc's length is a portion of a circle's diameter."
Therefore, we must first establish what percentage of the circle the specified arc length represents.
360° is a complete circle.
Thus, the fraction equals 7.2°/360°, or 1/50.
As a result, the stated arc length (800km) with a 7.2° central angle is 1/50th of the entire circle.
Thus, the whole circumference is 800 x 50, or 40000 km.
Alternately, you can calculate circumference using the formula below:
360° center angle x arc length as the circumference (theta)
Values substituted: circumference 800 = 360° 7.2°
circumference = 360°, 800°, and 7.2°, or 40000 kilometers
Therefore, the earth is 40000 kilometers around. There is no need to round off because the circumference already contains significant figures.
Learn more about Circumference
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