IXL - Find the component form of a vector given its magnitude and direction angle (Geometry practice)

The magnitude of a vector

is 22 and its direction angle

is 49°. Write the component form for

Round each component to the nearest hundredth.

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question

The magnitude of a vector

is 8 and its direction angle

is 20°. Write the component form for

Round each component to the nearest hundredth.

key idea

A vector is a quantity that has both a length and a direction.

The length of a vector

is called the magnitude, which is written

The direction of

can be specified by the counterclockwise angle

from the positive

-axis

called the direction

angle.

The component form of a vector

with direction angle

cos

(

)

sin

(

)

The first component,

cos

(

)

is the horizontal change, and the second component,

sin

(

)

is the vertical change.

solution

You are given

and

20°

Find the component form.

cos

(

𝜃

)

sin

(

𝜃

)

⟨

cos

(

)

sin

(

)

⟩

⟨

(

0.9396…

)

(

0.3420…

)

⟩

⟨

7.52

2.74

⟩

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Q.8Find trigonometric functions using a calculator

BB.3Find the component form of a vector

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