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Question
The amplitude of `sin pi/5 + i(1 - cos pi/5)` is ______.
Options
`(2pi)/5`
`pi/5`
`pi/15`
`pi/10`
Solution
The amplitude of `sin pi/5 + i(1 - cos pi/5)` is `underlinebb(pi/10)`.
Explanation:
Here, rcosθ = `sin (pi/5)` and rsinθ = `1 - cos pi/5`
Therefore, tanθ = `(1 - cos pi/5)/(sin pi/5)`
= `(2sin^2 (pi/10))/(2sin (pi/10).cos(pi/10))`
⇒ tanθ = `tan(pi/10)` i.e., θ = `pi/10`.
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