Download 13-8 Reciprocal Trigonometric Functions Evaluate and graph

Evaluate and graph reciprocal trigonometric functions by
applying rules for trigonometric functions.
 We know the trigonometric functions: sine, cosine, tangent
 The reciprocals of these functions have names:
1
= 𝑐𝑠𝑐𝜃
𝑠𝑖𝑛𝜃
1

= 𝑠𝑒𝑐𝜃
𝑐𝑜𝑠𝜃
1

= 𝑐𝑜𝑡𝜃
𝑡𝑎𝑛𝜃

this is the cosecant
this is the secant
this is the cotangent
 Find cot(−
5𝜋
)
6
without using a calculator
 This is the point (−
3
1
,− )
2
2
 Since we know that 𝑡𝑎𝑛𝜃 =
3

−2
1
−2
= 3
𝜋
6
 You try: find csc( )
2
on the unit circle
𝑠𝑖𝑛𝜃
𝑐𝑜𝑠𝜃
=
𝑦
𝑥
then the cotangent must be 𝑐𝑜𝑡𝜃 =
𝑥
𝑦
 Make sure you are in radian mode!
 Find sec(2)
 Secant is the reciprocal of cosine
 Type 1/cos(2)
 Round: sec(2) ≈ -2.403
 You try: find cot(10) to the nearest thousandth
 1.542
 Find csc(35°)
 You can change to degree mode OR leave in radian mode and type 1/sin(35°)
 You get the degree symbol by going to the ANGLE menu (above APPS)
 1.743
 Make a table of values
 Ex: sketch the graph of 𝑦 = csc 𝑥 from 0 𝑡𝑜 2𝜋
 csc is the reciprocal of sin
 Make a table for the graph of 𝑦 = sin 𝑥
X
0
𝝅
𝟑
Sin(x)
0
0.9
Csc(x)
---
1.2
𝝅
𝟐
1
𝟐𝝅
𝟑
0.9
1
1.2
0
𝟒𝝅
𝟑
-0.9
𝟑𝝅
𝟐
-1
𝟓𝝅
𝟑
-0.9
0
---
-1.2
-1
-1.2
---
𝝅
 Now include values of 𝑦 = csc 𝑥 which are
1
sin 𝑥
 Undefined wherever sin(x) = 0 so we have asymptotes
𝟐𝝅
 Odds p.888 #9-45