Monday, March 31, 2014
SP #7: Unit Q Concept 2: Finding All Trig Functions Using Identities
“Please see my SP7, made in collaboration with Eldon, by visiting their blog here. Also be sure to check out the other awesome posts on their blog”
Friday, March 28, 2014
I/D #3:Unit Q Concept 1:Pythagorean Identities
Inquiry Activity Summary:
An identity is a proven fact or formula that is always true. We will be showing you how the pythagorean theorem is an "identity" in my work below:
-Finding: (Sin^2x+Cos^2x=1)
-Pythagorean Theorem: x^2+y^2=r^2
-Sin=y/r; Cos=x/r
-Substitute the trig functions into the pythagorean theorem:
(y/r)^2+ (x/r)^2= 1
-equals the same thing as saying Sin^2x+Cos^2x=1
-We can then check it by lets say, using the 45degree angle in our Unit Circle.
-Coordinates are (rad2/2, rad2/2)
x y
-(rad2/2)^2+ (rad2/2)^2=1
-The radical in rad2 cancels, you square the 2 in the bottom and your left with
-(2/4)+(2/4)=1
-(4/4)=1
-Correct!
Inquiry Activity Reflection:
-The connections that i see between Units N, O, P, and Q so far are that they all have something to do with the unit circle, we have to derive stuff.
-Three words that I would describe trigonometry would be fascinating, hard, but doable.
An identity is a proven fact or formula that is always true. We will be showing you how the pythagorean theorem is an "identity" in my work below:
-Finding: (Sin^2x+Cos^2x=1)
-Pythagorean Theorem: x^2+y^2=r^2
-Sin=y/r; Cos=x/r
-Substitute the trig functions into the pythagorean theorem:
(y/r)^2+ (x/r)^2= 1
-equals the same thing as saying Sin^2x+Cos^2x=1
-We can then check it by lets say, using the 45degree angle in our Unit Circle.
-Coordinates are (rad2/2, rad2/2)
x y
-(rad2/2)^2+ (rad2/2)^2=1
-The radical in rad2 cancels, you square the 2 in the bottom and your left with
-(2/4)+(2/4)=1
-(4/4)=1
-Correct!
Inquiry Activity Reflection:
-The connections that i see between Units N, O, P, and Q so far are that they all have something to do with the unit circle, we have to derive stuff.
-Three words that I would describe trigonometry would be fascinating, hard, but doable.
Tuesday, March 18, 2014
WPP #13 & 14: Unit P Concept 6 & 7
Please see my WPP13-14, made in collaboration with Clyde, by visiting their blog here Also be sure to check out the other awesome posts on their blog.
Thursday, March 6, 2014
WPP #12: Unit O Concept 10: Angle of Elevation and Depression Word Problems
Part 1: Three Year Old Jake sees a cookie jar on top of the fridge. The angle of elevation from the ground in 29 degrees. The distance from Jake to the fridge id 12 feet. What is the height of the cookie jar on top of the fridge? (round to the nearest tenths place).
Part 2: After he successfully gets the cookie jar on top of the fridge, he spots his favorite little super awesome toy car. The height of the fridge would be ___ (Have to find the first part). The angle of depression is 32 degrees. What id the distance from Jake to his favorite little super awesome toy car?
Part 2: After he successfully gets the cookie jar on top of the fridge, he spots his favorite little super awesome toy car. The height of the fridge would be ___ (Have to find the first part). The angle of depression is 32 degrees. What id the distance from Jake to his favorite little super awesome toy car?
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| Part 1 |
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| Part 2 |
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