Respuesta :
well... you don't necessarily need to get the cosine value, in order to get the double angle
[tex]\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[/tex]
[tex]\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[/tex]
The value of cos 2[tex]\rm \theta[/tex] is -0.8432.
What are Trigonometric Ratios?
Trigonometric Ratios are the ratio of sides of a Right angled Triangle, used to determine the missing sides and angles of the triangle.
The trigonometric ratio sin[tex]\rm \theta[/tex] = 24/25
The value of cos 2[tex]\rm \theta[/tex] has to be determined.
The identity of cos 2[tex]\rm \theta[/tex] = 1- 2 sin²[tex]\rm \theta[/tex]
cos 2[tex]\rm \theta[/tex] = 1 - 2 * (24/25)²
cos 2[tex]\rm \theta[/tex] = 1 - 1.8432
cos 2[tex]\rm \theta[/tex] = -0.8432
To know more about Trigonometric Ratios
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