Pre-Calculus

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I will help with this.

ok

We know that the cos (135 degrees) = -sqrt(2)/2.

The half angle formula states that cos (x/2) = +/- sqrt [ (1 - cos s)/2 ]

So cos (67.5 degrees) = cos (135 degrees / 2)

it says simplify the answer including any radicals. Use integers or fractions for any numbers in the expression. rationalize all denominators.

= +/- sqrt [ (1 -cos(135 deg) ) / 2 ]

I will do that.

= +/- sqrt [ (1 - (-sqrt(2)/2 ) /2 }

= +/- sqrt [ (1 + sqrt(2)/2 ) /2]

= +/- sqrt [ (2 + sqrt(2) ) 2 ]

I meant: = +/- sqrt [ (2 + sqrt(2) ) / 2]

so 2 + sqrt 2 /2

hold on a minute. It's hard to input into the chat.

I keep hitting the enter key too fast. Let me write that last line carefully.

= +/- sqrt [ ( (2 + sqrt(2) )/2 ) /2 ]

there.

= +/- sqrt [ (2 + sqrt(2) ) /4 ]

= +/- sqrt (2 + sqrt (2) ) / 2

so 2 + sqrt 2 over 4

your confusing me

The 4 is in the denominator of the square root. So it "comes out of the square root as a 2.

so is the answer 2 + sqrt 2 over 2?

Remember the parentheses and the sqrt on top. This solution is a square root with another square root inside it. I will show it in a moment.

sqrt ( 2 + sqrt 2 )

2

it said that was wrong again

How are you writing it?

sqrt (2+sqrt2)/2

try: (sqrt(2 + sqrt(2))/2

no its not excepting that.

I apologize for typing this too fast. It should be

(sqrt(2-sqrt(2) ) / 2

is that the answer?

yes

ok thanks im not sure but i will except it.

Easier to see this way.

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