By using trigonometric identity, 8 cis 270° in binomial form (rectangular form) is -8i.
How to express in binomial form
To express "8 cis 270°" in binomial form (rectangular form), use the trigonometric identity:
cis(θ) = cos(θ) + i sin(θ)
Given:
Magnitude (r) = 8
Angle (θ) = 270°
Using the trigonometric identity, convert the given polar form to binomial form:
8 cis 270° = 8(cos(270°) + i sin(270°))
Now, evaluate the cosine and sine values for 270°:
cos(270°) = 0
sin(270°) = -1
Substituting these values
8 cis 270° = 8(0 + i(-1))
8 cis 270° = 8i(-1)
8 cis 270° = -8i
Therefore, "8 cis 270°" in binomial form (rectangular form) is -8i.
Complete question
Express in binomial form: 8 cis 270°.