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The School of Athens
Euclid, as imagined by Raphael in this detail from The School of Athens.
Jamshed Al-Kashi
Al-Kashi was one of the greatest mathematicians of the 15th century, calculating the sin(1*) correct to 16 decimal places.
Al-Beruni
The 11th century scientist and philosopher managed to estimate the radius of the earth using a very creative method that employed trigonometry.
9 comments:
I have a question on the hw due May 5. for number 8 part b, I found t, but am not sure how Mr. kerai found the radians. Could someone explain? Thanks.
i am confused about that too- i tried using some of the ratios but i didn't get the answers
That question only really asks for one answer, so isn't the first number all we need?
technically yes, but Mr. Kerai wrote a second one and I wanted to know how he arrived at his answer.
I have another question. Is arc length measured in radians or is that arc measure?
For 8 b on that HW assignment, I am asking for angles that will give you a specific length. The unit circle given to you is already calibrated in radians, which should be obvious given that 180 degrees is marked off by 3 and some stuff. So now given a sine or cosine length, you have to find the angles, in radians, that correspond to those lengths. You've been doing this all along except in this case you have no calculator to use, you instead have the approximate reading you can get from the diagram.
Virginia, the circle given to you IS the unit circle. You don't need ratios. Compare your unit circle handout to the diagram in 8 b and look at the obvious connection. I am not asking about special angles in question 8 and that might be throwing you off.
I have given two answers because there are two answers within 360 degrees or 2Pi radians and so in case you chose one of them, then you can make sure that it corresponds to one of my answers.
Victoria, your arc length question is unclear. radian measure is a measure of arc length, but on a unit circle. On another circle you'll have to multiply it by whatever the radius is. I mean that is how we can safely find arc lengths on circles of different radii. Look at all the conversion question we have done.
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