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Aim: What are the Co-functions and Quotient Identities in Trigonometry?. Do Now:. =. Reciprocal Identities. Quotient Identities. Use in verification of identities and in numerical calculations. Verify the Identity. A trig identity is an equation that is true for all values of variable. I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
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1. Aim: What are the Co-functions and Quotient Identities in Trigonometry? Do Now: =

2. Reciprocal Identities Quotient Identities Use in verification of identities and in numerical calculations

3. Verify the Identity A trig identity is an equation that is true for all values of variable. verify

4. Reciprocal Identity Quotient Identity What does simplifying mean? Simplifying a trig expressions usually means expressing in terms of sine and cosine.

5. usually written (sin )2 = sin2 Model Problems Write an expression in terms of sin , cos , or both. Simplify whenever possible. 1. sec  • cot  2.

6. Calculator: 1 ÷ tan ) x2 ENTER 30 Display: 3 Model Problems Find the exact numerical value for each: 1. cot2 30º

7. Model Problems Find the exact numerical value for each: 2. cot 45º • csc 45º tan 45º = 1 cot 45º= 1 cot 45º • csc 45º 1 •

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

9. Co- sin  = cos(90º – ) cos  = sin(90º – ) Co- tan x = cot(90º – x) cot x = tan(90º – x) Model Problems Write in terms of the co-function the sine of 30o. • If x and y are the measures of two acute angles and tan x = cot y, then • x = y + 90 2) x = y – 90 • 3) x = 90 – y 4) y =x – 90 y = (90º – x)

10. 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 = 35º x + 20º = 55º √ cos 55º = .57357… sin 35º = .57357…

11. Which expression is NOT equal to the other three expressions? Model Problems