Table of Contents 2 Angles and their Measures

Table of Contents 2. Angles and their Measures continued

Angles and their Measures continued Essential question – What are other operations to be done for angles?

What quadrant is it in? • To find out what quadrant an angle is in – Make a negative angle positive by adding 360 o or 2π (may need to do multiple times) – If angle is bigger than 360 o or 2π, make it smaller by subtracting 360 o or 2π (may need to do multiple times) – Figure out what quadrant it is in based on angles of axes (from yesterday) – If the question asks you to sketch the angle, • draw the terminal side in the right quadrant • go in either positive or negative direction based on original problem • if you have added or subtracted 360 o or 2π, you need to go around multiple times.

What quadrant is it in (and sketch)?

What quadrant is it in? (radians) • • Follow steps to make small positive angle Put fraction in calculator (without the π) If answer is < 0. 5, it is in 1 st quadrant If answer is between 0. 5 and 1, it is in 2 nd quadrant • If answer is between 1 and 1. 5, it is in 3 rd quadrant • If answer is between 1. 5 and 2, it is in 4 th quadrant

Examples – which quadrant? (radians) (and sketch)

Complementary/Supplementary • Complementary angles add up to 90 o (or π/2 for radians) o • Supplementary angles add up to 180 (or π for radians)

Examples • What angle is complementary/supplementary to 36 o ? • What angle is o complementary/supplementary to 110 ?

Examples - radians • What angle is complementary/supplementary to ? ?

Reference Angles • A reference angle is the acute angle that an angle makes with the x-axis •

Finding Reference Angles • Follow steps to make small positive angle • Find out which quadrant it is in • In the 1 st quadrant, the reference angle is the SAME as the angle itself • In the 2 nd quadrant subtract the angle from 180 o or π • In the 3 rd quadrant subtract 180 o or π from the angle • In the 4 th quadrant subtract the angle from 360 o or 2π

Examples • • Find the reference angle for the following angles. 37 o 7π/4 -2π/3 -190 o 17π/7 820 o

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