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Chapter 2: Q5E (page 71)

The matrix

[鈭�0.8鈭�0.60.6鈭�0.8]

Represents a rotation. Find the angle of rotation (in radians).

Short Answer

Expert verified

The angle of rotation is 2.5 radians approx.

Step by step solution

01

Transformation

Given T is a linear transformation fromR2鈫�R2.

Then we can write the transformation.

T(rcos伪,rsin伪)=(rcos(伪+胃),rsin(伪+胃))=(rcos伪cos胃鈭�rsin伪sin胃,rsin胃cos伪+rcos胃sin伪)=cos胃鈭�sin胃sin胃cos胃rcos伪rsin伪[T]尾=cos胃鈭�sin胃sin胃cos胃

02

Value of angle

Now, equate the obtained transformation with the given matrix.

cos胃鈭�sin胃sin胃cos胃=鈭�0.8鈭�0.60.6鈭�0.8

Now on to solving the above equations.

cos胃=鈭�0.8胃=2.498radians

Hence, the angle of rotation is 2.5 radians approx.

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Most popular questions from this chapter

Consider the circular face in the accompanying figure. For each of the matrices A in Exercises 24 through 30, draw a sketch showing the effect of the linear transformation T(x)鈫�=Ax鈫�on this face.

26.[0110]

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TRUE OR FALSE?

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TRUE OR FALSE?

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