1. Do Now
What does SOHCAHTOA represent written out fully?

2. Chapter 2 Acute Angles & Right Triangles
Section 2.1 – Trigonometric Functions of Acute Angles
Objective: SWBAT use definitions of Trigonometric Functions and Cofuntions to find measurements of triangles.

3. Review Right-triangle Based Definitions of Trigonometric Functions
For any acute angle A in standard position.

4. Review Finding Trig Functions of Acute Angles
Find the values of sin A, cos A, and tan A in the right triangle shown. A C B 52 48 20

5. Review Finding Trig Functions of Acute Angles
Find the values of sin A, cos A, and tan A in the right triangle shown. A C B 52 48 20

6. Cofunctions
Did you happen to notice that sin A = cos B from our last example? Did you happen to notice that cos A = sin B from our last example? Do you recognize that angles A and B are complementary?
Since angles A and B are complementary and sin A = cos B, the functions sine and cosine are called cofunctions.

7. Cofunction Identities
For any acute angle A,
sin A = cos(90  A) csc A = sec(90  A)
tan A = cot(90  A) cos A = sin(90  A)
sec A = csc(90  A) cot A = tan(90  A)

8. Write Functions in Terms of Cofunctions
Write each function in terms of its cofunction.
a) cos 38
cos 38 = sin (90  38) = sin 52
b) sec 78
sec 78 = csc (90  78) = csc 12

9. Write Functions in Terms of Cofunctions
Write each function in terms of its cofunction.
a) cos 52
cos 52 = sin (90  52) = sin 38
b) tan 71
tan 71 = cot (90  71) = cot 19

10. SOLVING EQUATIONS USING THE COFUNCTION IDENTITIES
Find one solution for the equation
Assume all angles are acute angles. Since Cot and Tan are cofunctions this is only true if the sum of the angles = 90°

11. SOLVING EQUATIONS USING THE COFUNCTION IDENTITIES
Find one solution for the equation. Assume all angles involved are acute angles.
(a)
Since sine and cosine are cofunctions, the equation is true if the sum of the angles is 90º.

12. SOLVING EQUATIONS USING THE COFUNCTION IDENTITIES (continued)
Find one solution for the equation. Assume all angles involved are acute angles.
(b)
Since tangent and cotangent are cofunctions, the equation is true if the sum of the angles is 90º.

13. Increasing/Decreasing Functions
As A increases, y increases and x decreases.
Since r is fixed,
csc A decreases
sin A increases
sec A increases
cos A decreases
cot A decreases
tan A increases

14. Tell whether each statement is true of false.

15. Homework
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