what is two angles measuring [tex] \pi /8[/tex] and [tex] 7\pi/8[/tex] radians?
Question
Answer:
Answers:__________________________________
Question 1) "22.5° " .
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Question 2) "157.5° " .
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Note of interest: "22.5° + 157.5° = 180° " .
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Explanation:
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To convert from "radians" to "degrees" , we multiply the:
"value in radians" by "180/[tex] \pi [/tex]"
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Question 1) (π/8) * (180/π) = ?
Both of the "π" values cancel out to "1" {since "π/π = 1" } ;
and the "180" changes to "45" ; and the "8" changes to "2" ;
→ since "(180/8)" = "(180÷4) / (8÷4) = 45/2 ;
→ So we have: "45/2" ;
→" 45/2 = 45/ 2 = 22.5 degrees.
The answer is: 22.5° .
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Question 2) Convert " (7π /8)" to degrees .
Note: "(7π /8)" = 7 * (π/8) " .
We know that "(π/8)" in degrees is: 22.5° (from question #1).
Multiply this value by "7", to get the answer.
22.5° (7) = 157.5° .
The answer is: 157.5° .
Isn't math fun, sometimes??
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