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kow [346]
1 year ago
9

Hi, teacher I was absent these days and I didn’t understand anything about this lesson and I need help this is not count as a te

st it’s just hw please help thanks a lot The first question I need help, use cod 210 degree =-radical 3 over 2 to find the exact value of cod 105 degree

Mathematics
1 answer:
motikmotik1 year ago
4 0

Given:

There are given that the cos function:

cos210^{\circ}=-\frac{\sqrt{3}}{2}

Explanation:

To find the value, first, we need to use the half-angle formula:

So,

From the half-angle formula:

cos(\frac{\theta}{2})=\pm\sqrt{\frac{1+cos\theta}{2}}

Then,

Since 105 degrees is the 2nd quadrant so cosine is negative

Then,

By the formula:

\begin{gathered} cos(105^{\circ})=cos(\frac{210^{\circ}}{2}) \\ =-\sqrt{\frac{1+cos(210)}{2}} \end{gathered}

Then,

Put the value of cos210 degrees into the above function:

So,

\begin{gathered} cos(105^{\circ})=-\sqrt{\frac{1+cos(210)}{2}} \\ cos(105^{\operatorname{\circ}})=-\sqrt{\frac{1-\frac{\sqrt{3}}{2}}{2}} \\ cos(105^{\circ})=-\sqrt{\frac{2-\sqrt{3}}{4}} \\ cos(105^{\circ})=-\frac{\sqrt{2-\sqrt{3}}}{2} \end{gathered}

Final answer:

Hence, the value of the cos(105) is shown below:

cos(105^{\operatorname{\circ}})=-\frac{\sqrt{2-\sqrt{3}}}{2}

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