13.2 – Define General Angles and Use Radian Measure

0°0° 90° 180° 270° Initial side Terminal side Standard Position:Vertex at origin and initial side is on x-axis

1.Draw an angle with the given measure in standard position 65°

1.Draw an angle with the given measure in standard position 230° 40° 50°

1.Draw an angle with the given measure in standard position 495° 135°45°

1.Draw an angle with the given measure in standard position –60° 60°

Radian: Measure of an angle in standard form whose terminal side intercepts an arc of length r C = 2πr2πr So there are 2π radians in a circle

Converting Degrees and Radians Degrees  Radians Radians  Degrees

2. Convert the degree into radians. 30° ° 4 3

3. Convert the radians into degrees ° 45 –225°

0 π2π2 π 3π 2 45° π4π4 135° 3π 4 315° 225° 5π 4 7π 4 2π2π

0 π2π2 π 3π 2 30° π6π6 120° 5π 6 300° 150° 7π 6 11π 6 60° π3π3 2π2π 2π 3 4π 3 5π 3 330° 240° 210°

4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem. sin 30° 30° 1 2 =

4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem. cos 45° 45° 1 1 =

4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem. tan 30° = 30° 1 2

4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem. csc 60°= 60° 1 2

4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem. sec 60°= 60° 1 2

4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem. cot 45°= 45° 1 1

4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem. = 1 2

= 1 1

= 1 2 =

5. Evaluate the following trigonometric functions with a calculator. Round answers to four decimal places. Remember to change the mode of your calculator. sin 55°  cos 135°  – sec 315°  = cot 76°  =

5. Evaluate the following trigonometric functions with a calculator. Round answers to four decimal places. Remember to change the mode of your calculator.    =  –2 =