Aim: What are the reciprocal functions and cofunction? Do Now: In , 90 , C ABC AB = 17 and BC = 15. 1) Find A sin A cos A tan a) AC b) c) d) 2) Find the reciprocal of A sin A cos A tan a) b) c) A B C Worksheet
Dec 30, 2015
Aim: What are the reciprocal functions and cofunction?
Do Now: In ,90, CABC AB = 17 and BC = 15.
1) Find
Asin Acos Atana) AC b)
c) d)
2) Find the reciprocal ofAsin Acos Atana) b) c)
A
BC
Worksheet
Asin Acos
Atan
1) a) AC = 8, b) = 15/17 c) = 8/17
= 15/8d)
Asin Acos
Atan
2) a) rec. of = 17/15 b) rec. of
c) rec. of = 8/15
= 17/8
When we write the reciprocal of sine, cosine and tangent, we get 3 other functions – the reciprocal functions.
We have names for those three reciprocal functions
adjacent
hypotenusesec
Definition of the reciprocal functions
opposite
hypotenusecsc
opposite
adjacentcot
sin
1csc
cos
1sec
tan
1cot
or
csc
1sin
or
or
sec
1cos
cot
1tan
Quadrant I II III IV sin + + – –
csc + + – –cos + – – +sec + – – +tan + – + –cot + – + –
Properties of all 6 trig functions
A
B C
30
Given ΔABC, mB = 30, find the values of a) sin B b) cos A
12
32
130sin
2
160cos
Then sin30 = cos60
That is sin30 = cos (90 – 30)
In general, sin A = cos (90 – A) or cos A = sin (90 – A)
The sine of an acute angle is equal to the cosine of its complement. The sine and cosine are cofunctions
tan A = cot (90 – A) cot A = tan (90 – A)
sec A = csc (90 – A) csc A = sec (90 – A)
tangent and cotangent are cofunctions
secant and cosecant are cofunctions
In all three pairs of cofunctions, the angles are complementary angles.
Relationship of all trig functions
sin
cos
tan
cot
sec
csc
cofunctions
cofunctions & reciprocal
cofunctions
reciprocal
reciprocal
Find a value of for which the statement is true.
1. cos17sin
2. )60cot(tan
3. )83csc()10sec(
4. )242cos(sin
sin cosWrite the following functions in terms of
, or both:
cot
sec
tan
csc
sin
a)
b)
c)
d)
150csc
240sec
3cot
3sec
3
2cot
Find the values of the followinga)
b)
c)
d)
e)
Determine the quadrant of the angle lie
0csc
0cot
0cot 0sin
0sec 0tan
a)
b)
c) and
d) and