Consider the vector v = (5,8).  Write v in the form (|v|cosθ|v|sinθ).

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crmhaske | College Teacher | (Level 3) Associate Educator

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We need to know the magnitude of v and the angle it makes with the x-axis.

To solve for magnitude:

`|v|=sqrt(5^2+8^2)=sqrt(89)`

For the angle it makes with the x axis:

`costheta=5/sqrt(89) -> theta=58`

Therefore, the vecotr in the form `(|v|costheta,|v|sintheta)`  is:

`(sqrt89cos58,sqrt89sin58)`

Sources:

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