Trigonometric Functions and Linear Transformations

To reflect points across an axis

To change the size of geometric shapes

To rotate points in the plane

To translate points in the plane

T(1,1) and T(0,0)

T(1,0) and T(0,1)

T(1,0) and T(1,1)

T(0,0) and T(0,1)

Secant

Sine

Cosine

Tangent

Cotangent of theta

Sine of theta

Cosine of theta

Tangent of theta

Negative cosine of theta

Cosine of theta

Negative sine of theta

Sine of theta

Because the x-coordinate is always negative

Because the rotation is counterclockwise

Because the y-coordinate is positive

Because the rotation is clockwise

By adding the coordinates

By multiplying the coordinates

By arranging them as rows

By arranging them as columns

Start with secant and differentiate

Start with tangent and differentiate

Start with cosine and differentiate

Start with sine and differentiate

-1

0

1

Either 1 or -1

√2

1/√2

0

1