1. Aim: What are the reciprocal functions and cofunction?
AB = 17 and BC = 15.
Do Now: In A
Find B C c) d)
a) AC b)
2) Find the reciprocal of a) b) c)
HW: Worksheet

2. 1) a) AC = 8, b) = 15/17 c) = 8/17 d) = 15/8 2) a) rec. of
= 17/ b) rec. of
= 17/8
c) rec. of
= 8/15
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

3. Definition of the reciprocal functions

4. or or or

5. Properties of all 6 trig functions
Quadrant I II III IV
sin – –
csc – –
cos – –
sec – –
tan – –
cot – –

6. Given ΔABC, mB = 30, find the values of a) sin B b) cos A2 1
30 B
Then sin30 = cos60 C
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

7. 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.

8. Relationship of all trig functions
reciprocal
cofunctions
cofunctions & reciprocal
reciprocal
cofunctions

9. Find a value of
for which the statement is true. 1. 2. 3. 4.

10. Find the values of the following a)b) c) d) e)

11. Determine the quadrant of the angle lieb)
and c) d)
and

12. Write the following functions in terms of , or both:a) b) c) d)