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 Coterminal angle – Angles that have the same terminal side

Positive angles Initial side on the positive x-axis and rotate counterclockwise

Negative angles Initial side on the positive x-axis and rotate clockwise

Quadrants Quadrant III Quadrant I Quadrant II Quadrant IV

Angles of the axes

Variables you will see for angle measures -

Examples What quadrant is the terminal side of the angle in? (Make a sketch of the angle)

Examples - Coterminal angles You can add or subtract multiples of 360 or -360 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

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 3600, this is the seconds

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

Radians Angle degrees can also be expressed in radians Radians 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

Examples Change from degrees to radians Change from radians to degrees

Coterminal Examples using radians Add or subtract 2π to angle

Complementary/Supplementary Complementary angles add up to 90 o or Supplementary angles add up to 180 o or

Examples What angle is complementary to 36 o ? What angle is supplementary to 36 o ? What angle is complementary to ? What angle is supplementary to ?

Finding arc lengths S=rθ S is arc length r = radius θ = central angle, must be in radians

Examples Find the length of the arc with radius 20 in and central angle of π/4 Find the length of an arc with radius 5 m and central angle of 180 o Find the measure of the central angle is arc length is 6 in and radius is 18 in θ = central angle

Assessment 321 –Write 3 new things you learned –Write 2 vocabulary words with their meaning –Write 1 thing you don’t understand