The Unit CircleChristina Myles

GeometryGrade 10

Click Pal to continue through

slideshow….

Welcome to Trigonometry, Class! Hey guys, it’s so

nice to see you again! I’m Pal and today, we will be discussing one of the most essential

concepts of trigonomentry: THE

UNIT CIRCLE! =)

So what IS the Unit Circle? Why is it so important? Let’s

find out!

Remember last week, when we

learned what SINE, COSINE,

AND TANGENT

were?

For Review, here are

some of the key

equations that we

discussed last week about the values of a

right triangle!

Did you know there was a

way to connect this to

the x and y axis of a graph??

THERE IS!

This is where the Unit Circle comes

into play!

We use it to help use find the x and y values

of the sine, cosine, and tangent of some

key angles!

Every degree and radian has its own corresponding value for x and y! where:

X = COS (θ)And

Y = SIN (θ)

And TAN (θ) = Y ÷ X

Degree Radian Sin (θ) = Y Cos (θ) = X Tan (θ) = Y/X

0o 0 0 1 030o π/6 1/2 (3)1/2/2 1/(3)1/2

45o π/4 1/ (2)1/2 1/ (2)1/2 1

60o π/3 (3)1/2/2 1/2 (3)1/2

90o π/2 1 0 ∞/DNE

Here are some of the most common angles and their

values. Let’s practice finding some values!

Looking at this unit circle,

what do you think the value for (x,y)

for 30o is?

Degree Radian Sin (θ) = Y Cos (θ) = X Tan (θ) = Y/X

0o 0 0 1 0

30o π/6 1/2 (3)1/2/2 1/(3)1/2

45o π/4 1/ (2)1/2 1/ (2)1/2 1

60o π/3 (3)1/2/2 1/2 (3)1/2

90o π/2 1 0 ∞/DNE

If you said x = (3)1/2/2And y = ½ then you were correct!

Now that we have

some experience with the circle and the chart, time for a

QUIZ!

Click to begin quiz

What is the (x, y) for θ = π/2??

(0, 1)(1, 0)

(½ , ½)

Click to See Unit

Circle

Click to See

Chart

Sorry, that wasn’t it!

What you picked wasn’t correct, but don’t give up! Try looking at the chart or the Unit Circle itself

for some clues!

Click to Return to Question

Click to return to question

What is the (x, y) for θ = π/2??

(0, 1)(1, 0)

(½ , ½)

Click to See Unit

Circle

Click to See

Chart

Degree Radian Sin (θ) = Y Cos (θ) = X Tan (θ) = Y/X

0o 0 0 1 0

30o π/6 1/2 (3)1/2/2 1/(3)1/2

45o π/4 1/ (2)1/2 1/ (2)1/2 1

60o π/3 (3)1/2/2 1/2 (3)1/2

90o π/2 1 0 ∞/DNE

Back

Sorry, that wasn’t it!

What you picked wasn’t correct, but don’t give up! Try looking at the chart or the Unit Circle itself

for some clues!

Click to Return to Question

Correct!!!!!

Congrats on Mastering the Unit Circle!

End!

PowerPoint Clip Art Bing Images

◦ Searches – (x,y) plane URL: http://

ts1.mm.bing.net/th?id=I4572014687356492&pid=1.3

◦ Searches – unit circle URL: http://

ts3.mm.bing.net/th?id=I4624318799809054&pid=1.3

References

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over