Table of Contents 1. Angles and their Measures

Angles and their Measures Essential question – What is the vocabulary we will need for trigonometry?

Make a table TermDefinitionPicture

Trigonometry vocabulary Initial side – start side of angle Terminal side – end side of angle Standard position – An angle whose initial side is on the positive x-axis

Positive angles An angle in standard position that rotates counterclockwise

Negative angles An angle in standard position that rotates clockwise

Coterminal Angles Angles that have the same terminal side

Quadrants Quadrant III Quadrant I Quadrant II Quadrant IV

Angles of the axes

Variables you will see for angle measures

Decimal degree vs. degree/minute/second Sometimes angles are not whole numbers When this happens, they take 2 forms –Degree decimal o –Degree/minute/second (DMS) 53 o 18’ 23” To change from DMS to decimals, divide the minutes by 60 and the seconds by 3600 and add all together To change from decimal to DMS, multiply decimal by 60 – this is the minutes, then multiply resulting decimal by 60, this is the seconds

Examples - DMS Convert to decimal 35 o 18’ 27” -142 o 54’ 32” Convert to DMS o o

Radians Angle measures can also be expressed in radians A radian is the ratio of the length of an arc to its radius Radians are expressed in terms of = 180 o To change from degrees to radians, multiply by and reduce. To change from radians to degrees, multiply by

Radians continued Radians can take 2 forms – an exact answer and an approximate decimal answer The exact answer has a in it and it is the usual way to see radians To find an exact answer with your calculator, do not put the in the calculator, only write it in the answer However, radians can also be written as a decimal without the

Angles of the axes

Examples Change from degrees to radians Change from radians to degrees

Coterminal angles You add or subtract multiples of 360 o (or 2π) to find coterminal angles Find 2 coterminal angles (one positive and one negative) for 35 o Find 2 coterminal angles (one positive and one negative) for -23 o Find 2 coterminal angles (one positive and one negative) for 740 o

Examples for radians Find a positive and negative coterminal angle