Which of the following shows a group of possible angles a triangle could have?
1 answer:
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Answer:
A
Step-by-step explanation:
Begin with Euler's formula. I am assuming youre aware of this if youre taking complex algebra? You can prove Euler's formula by doing a Maclaurin expansion of cosine, sine, and e^x. Euler's formula states that:
We can put the first complex number in exponetial form by noticing the input is 2pi/3. The second complex number has an input of pi/3. Therefore:
Then:
Simplify the coefficients to get:
When you divide exponentials, you subtract the exponents. Therefore:
Put it back into trigonemtric form using Euler's formula:
Cosine of pi/3 is 0.5, and sine of pi/3 is square root of 3 over 2. We have:
