Reciprocal Trig Functions

Section 13.8

The Reciprocal Functions

cosecant (csc θ)=

secant (sec θ)=

cotangent (cot θ)=

1

sin

1

cos

1

tan

Finding Trig Values by Using the Graphing Calculators

Procedure: 1) make sure that you are in the right

calculator mode (either radian or degree) 2) enter everything into the calculator

and hit ENTER ** if the function is a reciprocal one, you

must enter it as a reciprocal

Let’s try some…

Find the following trig values: 1) sin 40°

2) cos 115°

3) csc 78°

4) cot 212°

Let’s try some…

5) sin

6) sec

7) cot 3.25

8) tan -90°

Let’s try these…

suppose sin θ = . Find csc θ.

suppose sec θ = . Find cos θ.

suppose cot θ = . Find tan θ.

15

89

13

Let’s look at the graphs of the reciprocal functions…

sin & cscy y

cos & secy y

tan & coty y

Let’s find these values by using the graph…

sec 20°

csc 89°

cot 134°

Procedure…

1) type in and graph function (either )

2) convert degrees into radians (either pi or decimal)

3) press TRACE, type in the radian measurement, and press ENTER (the trig value is the y-value)

1/ sin( ),1/ cos( ),1/ tan( )X X X