Tweet
Login
Mathematics Crystal
You may switch between
tex
and
pdf
by changing the end of the URL.
Home
About Us
Materials
Site Map
Questions and Answers
Skills
Topic Notes
HSC
Integration
Others
Tangent
UBC
UNSW
Calculus Advanced
Challenges
Complex Numbers
Conics
Differentiation
Integration
Linear Algebra
Mathematical Induction
Motion
Others
Polynomial Functions
Probability
Sequences and Series
Trigonometry
/
QnA /
HSC /
2014-04-04 Sin 75 deg.tex
--Quick Links--
The Number Empire
Wolfram Mathematica online integrator
FooPlot
Calc Matthen
Walter Zorn
Quick Math
Lists of integrals
List of integrals of trigonometric functions
PDF
\documentclass[10pt]{article} \usepackage{amssymb,amsmath} \usepackage[hmargin=1cm,vmargin=1cm]{geometry} \begin{document} {\large 2014-04-04\quad$\sin 75^\circ$} \begin{align*} \text{\bf Q:}\quad&\text{Find $\sin 75^\circ.$}\\ \text{\bf A:}\quad&\sin 75^\circ\\ =&\sin(30^\circ+45^\circ)\\ =&\sin 30^\circ\times\cos 45^\circ+\cos 30^\circ\times\sin 45^\circ\\ =&\frac{~1~}{2}\times\frac{1}{\sqrt{2}}+\frac{\sqrt{3}}{2}\times\frac{1}{\sqrt{2}}\\ =&\frac{1+\sqrt{3}}{2\sqrt{2}}\\ =&\frac{1+\sqrt{3}}{2\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}\quad\text{(denominator rationalisation)}\\ =&\frac{\sqrt{2}+\sqrt{6}}{4}\quad\text{(exact value)}\\ =&0.9659\quad\text{(approx. for verification on a calculator).}\\ \end{align*} \end{document}