what is cos pi 4 cos pi 4 sqrt 2 2 refer to the explanation below for how to find the exact value without a calculator Explanation It is possible to find the exact value of cos pi 4 by constructing a right triangle with one angle set to pi 4 radians
Let s first convert to degrees The conversion ratio between degrees and radians is 180 pi pi 4 xx 180 pi 45 Now we must think of the special triangle that contains a 45 angle This would be the following triangle The definition of cos is adjacent hypotenuse Therefore our ratio is 1 sqrt 2 However often teachers want the denominator to be Cos 1 cos pi 4 pi 4 pi 180 0 pi 4 180 4 45 0 cos 1 cos pi 4 cos 1 cos 45 cos 1 cos 45 since cos theta cos theta
what is cos pi 4
what is cos pi 4
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Find The Exact Value Of The Following Cos 225 Degrees Homework Study
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Cos 5pi 4 1 sqrt 2 or sqrt 2 2 5pi 4 is an angle in Quadrant III and as such based on CAST its cos is negative How do you change 2 sin 7x cos 4x into a sum How do you solve sin 4x sin 2x 0 using the product and sum formulas How do you use the sum and double angle identities to find sin3x
In order to evaluate cos pi 4 pi 3 we need to use the compound angle formula for cos cos A B cosAcosB sinAsinB Pi means 180 Hence pi 4 means 180 4 which is 45 45 is a special triangle where the measurements are Now you can find the sine cosine and tangent without a calculator You should obtain Sin and cosine 1 sqrt2 Tangent 1 I am assuming you are familiar with the formula SOH CAH TOA yes
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Now it s just a matter of applying the definition of cos to find the wanted trig ratio cos adjacent hypotenuse cos 1 sqrt 2 or 0 707 as a fellow contributor stated However for the purpose of this problem I think your teacher would be looking for an exact value answer cos 7pi 4 1 sqrt 2 Hopefully this helps Identity color red bb cos A B cosAcosB sinAsinB RHS sqrt 2 cos pi 4 x sqrt 2 cos pi 4 cos x sin pi 4 sin x
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