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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
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