Write each function in terms of its cofunction.

WARM-UP

(a) cos 48° = sin (90° – 48°) = sin 42°

(b) tan 67° = cot (90° – 67°) = cot 23°

(c) sec 44°= csc (90° – 44°) = csc 46°

ID/Quadratic Quiz

Write all identities

1. Pythagoreans (3)

2. Quotients (2)

3. Cofunctions (6)

4. Reciprocal (6)

Solve the quadratics

5. x2 + 11x + 24 = 0

6. (x – 3)2 – 4 = 0

7. Write the quadratic formula.

Section/Topic 2.1b Trig Functions of Acute Angles

Objective (Trig Standard 9a)

Students will be able to apply trig concepts to right triangles using right-triangle-based definitions and cofunctions ID’s.

Homework (with announcements)

p68 (23 to 42, 59 to 64)Late start tomorrow

Trig Game PlanDate: 9/24/13

Increasing/Decreasing Functions

As A increases, y increases and x decreases.

Since r is fixed,

sin A increases csc A decreases

cos A decreases sec A increases

tan A increases cot A decreases

Example 1a COMPARING FUNCTION VALUES OF ACUTE ANGLES

Determine whether each statement is true or false.

(a) sin 21° > sin 18° (b) cos 49° ≤ cos 56°

(a) In the interval from 0 to 90, as the angle increases, so does the sine of the angle, which makes sin 21° > sin 18° a true statement.

(b) In the interval from 0 to 90, as the angle increases, the cosine of the angle decreases, which makes cos 49° ≤ cos 56° a false statement.

• Determine whether each statement is true or false.

(a) tan 25° < tan 23°

In the interval from 0° to 90°, as the angle increases, the tangent of the angle increases.

tan 25° < tan 23° is false.

(b) csc 44° < csc 40°

In the interval from 0° to 90°, as the angle increases, the sine of the angle increases, so the cosecant of the angle decreases.

csc 44° < csc 40° is true.

Example 1b COMPARING FUNCTION VALUES OF ACUTE ANGLES

30°- 60°- 90° Triangles

Bisect one angle of an equilateral to create two 30°-60°-90° triangles.

30°- 60°- 90° Triangles

Use the Pythagorean theorem to solve for x.

Example 2 FINDING TRIGONOMETRIC FUNCTION VALUES FOR 60°

Find the six trigonometric function values for a 60° angle.

Example 2 FINDING TRIGONOMETRIC FUNCTION VALUES FOR 60° (continued)

Find the six trigonometric function values for a 60° angle.

45°- 45° Right Triangles

Use the Pythagorean theorem to solve for r.

45°- 45° Right Triangles

adjacent

45°- 45° Right Triangles

Function Values of Special Angles

60

45

30

csc sec cot tan cos sin