Transcript comparing function values of acute angles

WARM-UP
Write each function in terms of its cofunction.
(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.
Trig Game Plan
Section/Topic
Objective (Trig
Standard 9a)
Date: 9/24/13
2.1b Trig Functions of Acute Angles
Students will be able to apply trig concepts to right
triangles using right-triangle-based definitions and
cofunctions ID’s.
Homework (with p68 (23 to 42, 59 to 64)
announcements) Late start tomorrow
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.
Example 1b
COMPARING FUNCTION VALUES OF
ACUTE ANGLES
• 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.
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

30
45
60
sin  cos  tan  cot  sec  csc 