z= 4+j3
using Pythagoreans theorem, r or |z| = 5
sin Θ = b/r = 3/5 = 0.75
/////// Here's where I'm confused /////////
0.75 = 36 ° 52'
I'm not sure how my teacher came to that conclusion, can someone point me in the right direction or show me the conversion process.
using Pythagoreans theorem, r or |z| = 5
sin Θ = b/r = 3/5 = 0.75
/////// Here's where I'm confused /////////
0.75 = 36 ° 52'
I'm not sure how my teacher came to that conclusion, can someone point me in the right direction or show me the conversion process.
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Hello,
When you have a complex z=a+ib
|z| = √(a² + b²)
Arg|z| = θ such as cos(θ)=a/|z| and sin(θ)=b/|z|
So in your case:
z = 4 + 3i
|z| = √(4² + 3²) = √(16 + 9) = √25 = 5
sin(θ) = 3/5 and cos(θ) = 4/5
Then
θ = sin⁻¹(3/5) = cos⁻¹(4/5) ≈ 36.86° ≈ 36° 52'
The errors in your description:
3/5 ≠ 0.75
You obviously forgot "sin⁻¹" and "cos⁻¹"
Regards,
Dragon.Jade :-)
When you have a complex z=a+ib
|z| = √(a² + b²)
Arg|z| = θ such as cos(θ)=a/|z| and sin(θ)=b/|z|
So in your case:
z = 4 + 3i
|z| = √(4² + 3²) = √(16 + 9) = √25 = 5
sin(θ) = 3/5 and cos(θ) = 4/5
Then
θ = sin⁻¹(3/5) = cos⁻¹(4/5) ≈ 36.86° ≈ 36° 52'
The errors in your description:
3/5 ≠ 0.75
You obviously forgot "sin⁻¹" and "cos⁻¹"
Regards,
Dragon.Jade :-)