Question

express as a single fraction the exact value of sin 75

Answer 1

sin75=sin(45+30)

Answer 2

sin 75 = sin(45 + 30) = sin 45 cos 30 + cos 45 sin 30
Can you simplify from here?

Answer 3

yupp thanks!

Answer 4

You're welcome :)

Answer 5

We got \(\sin 45 \cos 30+ \sin30 \cos45\)

\(\sin(30) = \frac{1}{2} \)
\(\sin(45) = \sqrt{\frac{1}{2}} \)
\(\cos(30) = \sqrt{\frac{3}{4}}\)
\(\cos(45) = \sqrt{\frac{1}{2}}\)

\(\large \begin{align} \ &=\sin 45 \cos 30+ \sin30 \cos45\\ \\ &= \sqrt{\frac{1}{2}} \sqrt{\frac{3}{4}}+\frac{1}{2}\sqrt{\frac{1}{2}}\\ &= \sqrt{\frac{1}{2}*\frac{3}{4}} + \frac{1}{2}\sqrt{\frac{1}{2}}\\ &= \sqrt{\frac{3}{8}}+ \frac{1}{2}\sqrt{\frac{1}{2}}\\ \end{align}\)

\(\large \begin{align} \ &= \frac{\sqrt{24}}{8}+\frac{1}{2}*\frac{\sqrt{2}}{2} \\ &= \frac{\sqrt{24}}{8}+\frac{\sqrt{2}}{4} \\ &= \frac{\sqrt{24}}{8}+\frac{2\sqrt{2}}{8} \\ &= \frac{2\sqrt{2}+\sqrt{4*6}}{8} \\ &= \frac{2\sqrt{2}+2\sqrt{6}}{8} \\ &= \frac{\sqrt{2}+\sqrt{6}}{4} \\ \end{align}\)

Answer 6

thank you! very clear response :)

Answer 7

From http://openstudy.com/study#/updates/4fd50096e4b057e7d22330d6

Answer 8

Uhh... @zepp
\[\sin(30) = \frac12\]\[\sin(45) = \frac{\sqrt{2}}{2}\]\[\cos(30) = \frac{\sqrt{3}}{2}\]\[\cos(45) = \frac{\sqrt{2}}{2}\]

Answer 9

Yeah, when you rationalize it.

Answer 10

Oh ok. Sorry. I didn't realize that. :)