Find the exact value of cos pi/16

2 Answers | Add Yours

embizze's profile pic

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

Posted on

Find the exact value of `cospi/16` .

We use a half-angle formula: `cos (alpha/2)=sqrt(1/2(1+cos alpha))`

(1) `cos pi/8=cos(pi/4)/2=sqrt(1/2(1+cos pi/4))`

`=sqrt(1/2(1+sqrt(2)/2))`

`=sqrt((2+sqrt(2))/4)`

`=sqrt(2+sqrt(2))/2`

(2) `cos pi/16 = cos (pi/8)/2`

`=sqrt(1/2(1+cos pi/8))`

`=sqrt(1/2((sqrt(2+sqrt(2)))/2))`

`=sqrt((2+sqrt(2+sqrt(2)))/4)`

`=(sqrt(2+sqrt(2+sqrt(2))))/2`

Thus `cos pi/16 = (sqrt(2+sqrt(2+sqrt(2))))/2~~.9807852804`

We’ve answered 318,928 questions. We can answer yours, too.

Ask a question