IXL - Find trigonometric ratios using multiple identities (Algebra 2 practice)

cot

(

)

and

0°

90°

what is

sin

(

)

Write your answer in simplified, rationalized form.

sin

(

)

ref_doc_title.

Learn with an example

question

csc

(

)

and

0°

90°

what is

cos

(

)

Write your answer in simplified, rationalized form.

cos

(

)

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
)

Pythagorean Identities:

sin

(

)

cos

(

)

tan

(

)

sec

(

)

cot

(

)

csc

(

)

The sign of a trigonometric function of

is determined by the quadrant

is in.

sin

(

)

cos

(

)

sin

(

)

cos

(

)

sin

(

)

cos

(

)

sin

(

)

cos

(

)

III

solution

Step 1:

First, 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

(

)

Step 2:

Now, use the Pythagorean identity

sin

(

)

cos

(

)

to find

cos

(

)

sin

(

)

cos

(

)

cos

(

)

Plug in

sin

(

)

Plug in

sin

(

)

cos

(

)

Square

cos

(

)

Subtract

from both sides

Subtract

from both sides

cos

(

)

Take the square root of both sides

So,

cos

(

)

–

Since

0°

90°

is in the first quadrant. So,

cos

(

)

is positive, which means that

cos

(

)

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LL.3Find trigonometric ratios using a Pythagorean or reciprocal identity

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