Question

Use an appropriate half-angle formula to find the exact value of the expression. cos(22. 5°)

Answer 1

The value of given trigonometric value cos(22. 5°) is 0.387.

According to the statement

we have given that the trigonometric value and we have to find the exact value of that given value with the help of the half angle formula.

So, For this purpose, we know that the

The half angle formulas are used to find the exact values of the trigonometric ratios of the angles like 22.5°.

So,

The given value is :

cos(22. 5°)

Then the value of cos half angle formula is

$cos (theta/2) = +- sqrt((1-cos theta) / 2)$

then

The value of θ/2 is 22.5 degree.

And θ is 22.5*2

θ = 45 degree

and cos 45 degree is 1/squareroot 2

And by this the value of given value become is

$cos 22.5 = +\sqrt{((\sqrt{2} -1)/(2 \sqrt{2} )) } = + 0.3827$

So, The value of given trigonometric value cos(22. 5°) is 0.387.

Learn more about half angle formulas here

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