I calculated \(\displaystyle{{\sin{{75}}}^{{\circ}}}\) as \(\displaystyle{\frac{{{1}}}{{{2}\sqrt{{{2}}}}}}+{\frac{{\sqrt{{{3}}}}}{{{2}\sqrt{{{2}}}}}}\), but

Erik Cantu 2022-03-31 Answered

I calculated sin75 as 122+322, but the answer is 2+64. What went wrong?
I calculated the exact value of sin75 as follows:
sin75=sin(30+45)
=sin30°cos45°+cos30°sin45°
=12·12+32·12
=122+322
The actual answer is
2+64

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Answers (1)

Esteban Sloan
Answered 2022-04-01 Author has 21 answers
They’re the same value. Multiply the numerator and denominator of your answer by 2 to see why.
1+322=221+322=2+64
You can also use sin45=cos45=22 (rationalizing 12) to get the answer more easily.
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