IXL - Inverses of csc, sec, and cot (Algebra 2 practice)

is an acute angle. Find the value of

in degrees.

sec

(

)

ref_doc_title.

Learn with an example

question

is an acute angle. Find the value of

in degrees.

csc

(

)

key idea

The cosecant

(

csc

)

of an acute angle in a right triangle is a ratio. It is the length of the hypotenuse

(

hyp

)

divided by the length of the opposite leg

(

opp

)

The hypotenuse is the side across from the right angle and the opposite leg is the side across from the specified angle.

csc

(

)

hyp

opp

solution

You are looking for an exact answer, so see if 2 is the cosecant

(

csc

)

of an angle from a 30°-60°-90° special triangle or a 45°-45°-90° special triangle.

You can use the definition of cosecant and the following reference triangles to calculate the cosecants of 30°, 45°, and 60°.

Find

csc

30°

60°

csc

30°

hyp

opp

Find

csc

45°

csc

45°

hyp

opp

Find

csc

60°

30°

csc

60°

hyp

opp

Since

csc

(

)

30°

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Work it out

Not feeling ready yet? These can help:

II.8Csc, sec, and cot of special angles

II.11Inverses of sin, cos, and tan: degrees

II.12Inverses of sin, cos, and tan: radians

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