Sin theta = 24/25, cos theta > 0, Find cos(2theta)

Mathematics Posted by admin

QUESTION POSTED AT 01/06/2020 - 04:15 PM

Answered by admin AT 01/06/2020 - 04:15 PM

Well... you don't necessarily need to get the cosine value, in order to get the double angle

\bf \textit{Double Angle Identities}
\\ \quad \\
sin(2\theta)=2sin(\theta)cos(\theta)
\\ \quad \\\\
cos(2\theta)=
\begin{cases}
cos^2(\theta)-sin^2(\theta)\\
\boxed{1-2sin^2(\theta)}\\
2cos^2(\theta)-1
\end{cases}
\\ \quad \\\\
tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\\\\
-------------------------------\\\\
cos(2\theta )=1-2sin^2(\theta )\qquad \qquad sin(\theta )=\cfrac{24}{25}
\\\\\\
cos(2\theta )=1-2\left( \cfrac{24}{25} \right)^2\implies cos(2\theta )=-0.8432
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