Jacob C. answered • 07/23/21
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(a) cos(30) = √3/2.
(b) sin(225) = sin(180 + 45) = -sin(45) = -1/√2
Jacob C.
Consider an equilateral triangle with each side of length 6. Each angle will be 60 degrees because it is equilateral. If we draw a line from a corner of the triangle to the midpoint of the opposing line, we will form a 30, 60, 90 triangle with one side length 6/2 = 3 and the hypotenuse 6. It’s straightforward to show, using the Pythagorean Theorem, that the remaining side length is 3sqrt(3). Thus, the cosine of the 30 degree angle is 3sqrt(3)/6 = sqrt(3)/2.
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Holly G.
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