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

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

Definition of the reciprocal functions

or or or

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

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

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 reciprocal cofunctions cofunctions & reciprocal reciprocal cofunctions

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

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

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

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