Aim What are the reciprocal functions and cofunction

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

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

Definition of the reciprocal functions

or or or

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

Given ΔABC, m B = 30 , find the values of a) sin B b) cos A 2 A 1 30 Then sin 30 = cos 60 B C That is sin 30 = 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 cofunctions & reciprocal cofunctions reciprocal

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

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

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

Determine the quadrant of the angle lie a) b) c) and d) and