The answer is:
Find the measure of x for this shape.A. 36b.28c.32d.22
1 answer:
let's recall that in an isosceles triangle, the twin sides make twin angles at the bottom/base, so on the triangle on the left-side, if the "vertex" atop has an angle of 116°, then the twin sides below are simply 180° - 116 = 64, split that in half and that's 32° each.
The same is true for the isosceles triangle on the right side. Also recall that a flat-line is always 180°, 32 + 72 + 76 = 180.
Check the picture below.
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Answer:
C,
Step-by-step explanation:
To remind you, Euler's formula gives a link between trigonometric and exponential functions in a very profound way:
Given the complex number , we want to try to get it in the same form as the right side of Euler's formula. As things are, though, we're unable to, and the reason for that has to do with the fact that both the sine and cosine functions are bound between the values 1 and -1, and 2√2 and -2√2 both lie outside that range.
One thing we could try would be to factor out a 2 to reduce both of those terms, giving us the expression
Still no good. √2 and -√2 are still greater than 1 and less than -1 respectively, so we'll have to reduce them a little more. With some clever thinking, you could factor out another 2, giving us the expression , and <em>now </em>we have something to work with.
Looking back at Euler's formula , we can map our expression inside the parentheses to the one on the right side of the formula, giving us
and
, or equivalently:
At this point, we can look at the unit circle (attached) to see the angle satisfying these two values for sine and cosine is 7π/4, so , and we can finally replace our expression in parentheses with its exponential equivalent:
Which is c on the multiple choice section.
