Find the exact value of cos pi/16
- print Print
- list Cite
Expert Answers
Eric Bizzell
| Certified Educator
briefcaseTeacher (K-12)
calendarEducator since 2011
write3,179 answers
starTop subjects are Math, Science, and Business
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`
Related Questions
- `cos(pi/16)cos((3pi)/16) - sin(pi/16)sin((3pi)/16)` Find the exact value of the expression.
- 2 Educator Answers
- `sin(pi/12)cos(pi/4) + cos(pi/12)sin(pi/4)` Find the exact value of the expression.
- 1 Educator Answer
- Find the exact value for sin 315 and csc(22*`pi`/3)
- 3 Educator Answers
- Find the exact value of log2 32
- 2 Educator Answers
- Find the exact value of cos 8*cos 38 + sin 8* sin 38
- 1 Educator Answer
jojdidjidji | Student
The square root of 69 is 8 some right?
cuz im been tryna work it out
Student Answers