TRIGONOMETRY

2.1 Angles in Standard Position

QUADRANTS

y

x

QUADRANT 1QUADRANT 2

QUADRANT 3 QUADRANT 4

QUADRANTS

VOCABULARY WORDS

initial arm

terminal arm

angle in standard position

reference angle

quadrantal angleambiguous case

INITIAL AND TERMINAL ARMS

• Angles are often interpreted as rotations of a ray

• The starting position and the final position are called the initial

arm and the terminal arm of the angle, respectively

ANGLE IN STANDARD POSITION

• its vertex is at the origin of a coordinate grid and its initial arm

coincides with the positive x-axis.

WHICH OF THESES ANGLES ARE IN STANDARD

POSITION?

WHICH OF THESES DIAGRAMS SHOWS AN ANGLE OF

70˚IN STANDARD POSITION?

REFERENCE ANGLE

• The acute angle (less than 90°) formed between the terminal arm

and the x-axis.

• The reference angle is always positive and measures between 0°

and 90°

The reference angle

for 230° is 50°

REFERENCE ANGLES

QUADRANT 1y

x

REFERENCE ANGLES

QUADRANT 2y

x

REFERENCE ANGLES

QUADRANT 3y

x

REFERENCE ANGLES

QUADRANT 4y

x

y

x

Draw and list all the possible angles in standard position with a

reference angle for 20°

Draw and list all the possible angles in standard position with a

reference angle for 20°

HOMEWORK

O PAGES: 83 - 84

O PROBLEMS: : 1 – 7, 9 – 10

O DUE on Tuesday, September 12

2.1 QUIZ

O TUESDAY September 12

O 10 – 15 minutes

Special Right Triangles

• For angles of 30°, 45°, and 60°, you can determine the exact values of trigonometric ratios.

1. Use the Pythagorean Theorem to find the length of

hypotenuse

2. Find the exact values of sin 45˚, cos 45˚, and tan 45˚

1. Use the Pythagorean Theorem to find the length of the

missing leg

2. Find the exact values of sin 30˚, cos 30˚, and tan 30˚

3. Find the exact values of sin 60˚, cos 60˚, and tan 60˚

Special Right Triangles

• MAKE A TABLE OF VALUES TO RECORD YOUR CALCULATIONS AND SPECIAL ANGLES

Trigonometric

Ratios

Exact Values for Special Angles

Special Right Triangles

• MAKE A TABLE OF VALUES TO RECORD YOUR CALCULATIONS AND SPECIAL ANGLES

Trigonometric

Ratios

Exact Values for Special Angles

sin

cos

tan

Special Right Triangles

• MAKE A TABLE OF VALUES TO RECORD YOUR CALCULATIONS AND SPECIAL ANGLES

Trigonometric

Ratios

Exact Values for Special Angles

30˚ 45˚ 60˚

sin

cos

tan