IXL - Find trigonometric ratios using a Pythagorean or reciprocal identity (Algebra 2 practice)

sin

(

)

and

0°

90°

what is

csc

(

)

Write your answer in simplified, rationalized form.

csc

(

)

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question

csc

(

)

and

0°

90°

what is

sin

(

)

Write your answer in simplified, rationalized form.

sin

(

)

key idea

Reciprocal Identities:

csc
(
θ
)
=
1
sin
(
θ
)
sec
(
θ
)
=
1
cos
(
θ
)
cot
(
θ
)
=
1
tan
(
θ
)

sin
(
θ
)
=
1
csc
(
θ
)
cos
(
θ
)
=
1
sec
(
θ
)
tan
(
θ
)
=
1
cot
(
θ
)

The sign of a trigonometric function of

is determined by the quadrant

is in.

sin

(

)

cos

(

)

sin

(

)

cos

(

)

sin

(

)

cos

(

)

sin

(

)

cos

(

)

III

solution

Use the reciprocal identity

sin

(

)

csc

(

)

to find

sin

(

)

sin

(

)

csc

Plug in

csc

(

)

Plug in

csc

(

)

To divide, multiply by the reciprocal

Multiply

So,

sin

(

)

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Not feeling ready yet? These can help:

II.6Find trigonometric ratios using the unit circle

HH.4Quadrants

A.6Simplify complex fractions

A.8Square roots

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