When I do the math myself, cos(7pi/4) = 0.995399899343688 However, when I plug cos(7pi/4) into a calculator such as WolframAlpha, it returns ` `` `` ``1/sqrt(2)` . Which is the correct answer and...

When I do the math myself, cos(7pi/4) = 0.995399899343688

However, when I plug cos(7pi/4) into a calculator such as WolframAlpha, it returns ` `` `` ``1/sqrt(2)` . Which is the correct answer and why? If `1/sqrt(2)` is correct how do I go about getting that answer?

 

Thanks :)

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embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

The reason you are getting the incorrect answer is that your caclculator is in degree mode instead of radian mode. This is a very common mistake, especially in a trigonometry class when you often switch modes from problem to problem.

When you switch to radian mode, you will get the approximate decimal expansion .7071067812 If your calculator gives results in radical form it will probably return `sqrt(2)/2` . (This is equivalent to `1/sqrt(2)` ; it is in simplified form. Most advanced books list `1/sqrt(2)` instead of `sqrt(2)/2` -- you will need to discuss with your instructor which is desired.)

Solving using right triangles or trigonometric identities will get the exact answer without a calculator.

pramodpandey's profile pic

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

`pi` is irrational number ,it depends on approximation and so many other factors.

Here in our question

`cos((7pi)/4)=cos(pi+(3pi)/4)`

`=-cos((3pi)/4)`

`=-cos(pi/2+pi/4)`

`=sin(pi/4)`

`=1/(sqrt(2))`

Theoretically you can verify it.

consider an isosceles right angle trianle of side unit length.So by Pythagoras Theorem , its hypotenuse will be `sqrt(2)` ,

`180^o=pi rad`

`45^o=(pi/4) rad`

`sin(pi/4)=(side)/(hypotenuse)`

`=1/(sqrt(2))`

(bot sides are equal in isosceles triangle, hyoptenuse is different)

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