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

1) a) AC = 8, b) = 15/17 c) = 8/17 = 15/8 d) 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

Definition of the reciprocal functions

or

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

A B C 30  Given ΔABC, m  B = 30 , find the values of a) sin B b) cos A 1 2 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 cofunctions cofunctions & reciprocal cofunctions reciprocal

Find a value of 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