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Exact value of
given
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u
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Value of
, u =
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Solution:  

Trigonometric double angle calculator that returns exact values and steps given one ratio and quadrant.
The formulas for double angle identities are as follows:

\text{sin(2u)}=2\cdot \text{sin(u)}\cdot \text{cos(u)}

\text{cos(2u)}=1-2\text{sin}^2\text{(u)}

\text{tan(2u)}=\frac{2\text{tan(u)}}{1-\tan ^2\text{(u)}}

\text{csc(2u)}=\frac{1}{2\cdot \text{sin(u)}\cdot \text{cos(u)}}

\text{sec(2u)}=\frac{1}{1-2\text{sin}^2\text{(u)}}

\text{cot(2u)}=\frac{1-\tan ^2\text{(u)}}{2\text{tan(u)}}



If given one trigonometric function, its value, and its quadrant, you can find the exact value of every double angle identity. For example, if told to find the exact value of sin2u given $\text{sec(u)}=\frac{9}{2}$, for $0\leq\text{u}\leq\frac{\pi}{2}$ (u is in quadrant 1). You may begin solving the problem by examining the equation for sin2u. According to the formula for sin2u, the values sinu and cosu must be known. The second part of the problem is finding the exact values of sinu and cosu using the given value, secu. We know that sec = $\frac{\text{hypotenuse}}{\text{adjacent}}$, the only unknown value is the opposite side length. This can be calculated by using the pythagrean theorem which states:

\text{opposite}=\sqrt{\text{hypotenuse}^2-\text{adjacent}^2}

\text{opposite}=\sqrt{\text{(9)}^2-\text{(2)}^2}

\text{opposite}=\sqrt{77}

\text{(in simplest form)}


Now that the opposite side length is known, we can find the values of sinu and cosu:

\text{sin}=\frac{\text{opposite}}{\text{hypotenuse}}

\text{sin}=\frac{(\sqrt{77})}{(9)}

\text{(in simplest form)}

\text{cos}=\frac{\text{adjacent}}{\text{hypotenuse}}

\text{cos}=\frac{(2)}{(9)}

\text{cos}=\frac{2}{9}

\text{(in simplest form)}

The final part of the double angle calculation process is substituting the found sin and cos values into the formula for sin2u as follows:

\text{sin2u}=2\cdot \text{sinu}\cdot \text{cosu}

\text{sin2u}=2\cdot (\frac{\sqrt{77}}{9})\cdot (\frac{2}{9})

\text{sin2u}=\frac{4\sqrt{77}}{81}

\text{(in simplest form)}

The final value of sin2u is $\frac{4\sqrt{77}}{81}$.
Double Angle Calculator Tutorial With Given

You must begin by choosing the identity you would like to calculate from the dropdown list. Once the identity has been chosen you have to chose the given function and ratio. for example: $\tan=\frac{5}{8}$. Once a function and ratio are known you may choose the quadrant of the central angle. The central angle must be a valid one otherwise the calculation will not work. If using sin or cos, the absolute value of these ratios must be greater than 0 and less than 1. If using tan or cot, the absolute value of the ratio can be any value. If using any other function, the absolute value of the ratio must be greater than 1.

Without Given

Using the double angle identity without a given value is a less complex process. You simply choose the identity from the dropdown list and choose the value of U which can be any value. for example: $\csc2\cdot8=0.2756373558169992$.


Check out another tutorial