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

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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! =)

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

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

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

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

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This is where the Unit Circle comes into play!

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

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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

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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!

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

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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!

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

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

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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

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Click to return to question

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

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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

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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

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Congrats on Mastering the Unit Circle! End!

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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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