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Christina Myles Geometry Grade 10 Click Pal to continue through slideshow….

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Presentation on theme: "Christina Myles Geometry Grade 10 Click Pal to continue through slideshow…."— Presentation transcript:

1 Christina Myles Geometry Grade 10 Click Pal to continue through slideshow….

2 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! =)

3 So what IS the Unit Circle? Why is it so important? Let’s find out!

4 Remember last week, when we learned what SINE, COSINE, AND TANGENT were?

5 For Review, here are some of the key equations that we discussed last week about the values of a right triangle!

6 Did you know there was a way to connect this to the x and y axis of a graph?? THERE IS!

7 This is where the Unit Circle comes into play!

8 We use it to help use find the x and y values of the sine, cosine, and tangent of some key angles!

9 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

10 DegreeRadianSin (θ) = YCos (θ) = XTan (θ) = Y/X 0o0o 0010 30 o π/61/2(3) 1/2 /21/(3) 1/2 45 o π/41/ (2) 1/2 1 60 o π/3(3) 1/2 /21/2(3) 1/2 90 o π/210∞/DNE Here are some of the most common angles and their values. Let’s practice finding some values!

11 Looking at this unit circle, what do you think the value for (x,y) for 30 o is?

12 DegreeRadianSin (θ) = YCos (θ) = XTan (θ) = Y/X 0o0o 0010 30 o π/61/2(3) 1/2 /21/(3) 1/2 45 o π/41/ (2) 1/2 1 60 o π/3(3) 1/2 /21/2(3) 1/2 90 o π/210∞/DNE If you said x = (3) 1/2 /2 And y = ½ then you were correct!

13 Now that we have some experience with the circle and the chart, time for a QUIZ! Click to begin quiz

14 (0, 1) (1, 0) (½, ½) Click to See Unit Circle Click to See Chart

15 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

16 Click to return to question

17 (0, 1) (1, 0) (½, ½) Click to See Unit Circle Click to See Chart

18 DegreeRadianSin (θ) = YCos (θ) = XTan (θ) = Y/X 0o0o 0010 30 o π/61/2(3) 1/2 /21/(3) 1/2 45 o π/41/ (2) 1/2 1 60 o π/3(3) 1/2 /21/2(3) 1/2 90 o π/210∞/DNE Back

19 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

20 Congrats on Mastering the Unit Circle! End!

21  PowerPoint Clip Art  Bing Images ◦ Searches – (x,y) plane  URL: http://ts1.mm.bing.net/th?id=I4572014687356492&p id=1.3 http://ts1.mm.bing.net/th?id=I4572014687356492&p id=1.3 ◦ Searches – unit circle  URL: http://ts3.mm.bing.net/th?id=I4624318799809054&p id=1.3 http://ts3.mm.bing.net/th?id=I4624318799809054&p id=1.3 Click to start show over


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