1. Aim: Co-functions & Quotient Identities Course: Alg. 2 & Trig. Aim: What are the Co-functions and Quotient Identities in Trigonometry? Do Now: =

2. Aim: Co-functions & Quotient Identities Course: Alg. 2 & Trig. Reciprocal Identities Quotient Identities Use in verification of identities and in numerical calculations

3. Aim: Co-functions & Quotient Identities Course: Alg. 2 & Trig. Verify the Identity A trig identity is an equation that is true for all values of variable. verify

4. Aim: Co-functions & Quotient Identities Course: Alg. 2 & Trig. What does simplifying mean? Reciprocal Identity Quotient Identity Simplifying a trig expressions usually means expressing in terms of sine and cosine.

5. Aim: Co-functions & Quotient Identities Course: Alg. 2 & Trig. Model Problems Write an expression in terms of sin , cos , or both. Simplify whenever possible. 1. sec  cot  2. (sin  ) 2 = sin 2  usually written

6. Aim: Co-functions & Quotient Identities Course: Alg. 2 & Trig. Model Problems Find the exact numerical value for each: 1. cot 2 30º 1 tan ENTER Display: 3 ÷ 30 Calculator: )x2x2

7. Aim: Co-functions & Quotient Identities Course: Alg. 2 & Trig. Model Problems Find the exact numerical value for each: 2. cot 45º csc 45º tan 45º = 1 1 cot 45º csc 45º cot 45º= 1

8. Aim: Co-functions & Quotient Identities Course: Alg. 2 & Trig. Trigonometry Co-functions sin  = cos(90º –  )cos  = sin(90º –  ) Co- sine  cosine tan  = cot(90º –  )cot  = tan(90º –  ) Co- tangent  cotangent sec  = csc(90º –  )csc  = sec(90º –  ) Co- secant  cosecant An trigonometric function of an acute angle is equal to the co-function of its complement.

9. Aim: Co-functions & Quotient Identities Course: Alg. 2 & Trig. Model Problems Write in terms of the co-function the sine of 30 o. sin  = cos(90º –  )cos  = sin(90º –  ) Co- If x and y are the measures of two acute angles and tan x = cot y, then 1)x = y + 902) x = y – 90 3) x = 90 – y 4) y = x – 90 tan x = cot(90º – x)cot x = tan(90º – x) Co- y = (90º – x)

10. Aim: Co-functions & Quotient Identities Course: Alg. 2 & Trig. Model Problem If sin x = cos(x + 20º) and x and (x + 20º) are the measure of two acute angles, find x. sine and cosine are co-functions If the sine of an acute angle is equal to the cosine of another acute angle, the angles must be complementary. x + 20º + x = 90º 2x + 20º = 90º 2x = 70º x = 35ºx + 20º = 55º sin 35º =.57357… cos 55º =.57357… √

11. Aim: Co-functions & Quotient Identities Course: Alg. 2 & Trig. Model Problems Which expression is NOT equal to the other three expressions?