The point (1, −1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.

Given: terminal side point

(

−

1

,

1

)

The point

(

−

1

,

1

)

is in the 2nd quadrant.

It has the

x

value

=

−

1

and the

y

-value

=

1

. Drop the point to the

x

-axis and form a reference triangle.

Using the Pythagorean Theorem

r

=

√

(

−

1

)

2

+

1

2

=

√

2

sin

θ

=

y

r

=

1

√

2

=

1

√

2

⋅

√

2

√

2

=

√

2

2

cos

θ

=

x

r

=

−

1

√

2

=

−

1

√

2

⋅

√

2

√

2

=

−

√

2

2

tan

θ

=

y

x

=

1

−

1

=

−

1

csc

θ

=

1

sin

θ

=

r

y

=

√

2

1

=

√

2

sec

θ

=

1

cos

θ

=

r

x

=

√

2

−

1

=

−

√

2

cot

θ

=

1

tan

θ

=

x

y

=

−

1

1

=

−

1

-2

7 - 9 = -2

reversed:

-2 + 9 = 7