Table of Contents 2. Angles and their Measures - continued

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Presentation transcript:

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 360o or 2π (may need to do multiple times) If angle is bigger than 360o or 2π, make it smaller by subtracting 360o 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 360o 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 1st quadrant If answer is between 0.5 and 1, it is in 2nd quadrant If answer is between 1 and 1.5, it is in 3rd quadrant If answer is between 1.5 and 2, it is in 4th quadrant

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

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

Examples What angle is complementary/supplementary to 36o ?

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 1st quadrant, the reference angle is the SAME as the angle itself In the 2nd quadrant subtract the angle from 180o or π In the 3rd quadrant subtract 180o or π from the angle In the 4th quadrant subtract the angle from 360o or 2π

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

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