Shall We Dance ??

Sorry for the EXTREMELY late post guys… I had to go the McDonald's Amazing Race in St. Vital Mall… But my team lost… L Apologies for any mistakes made in the post since I had my first lesson on identities today. If there are any mistakes, please tell me right away. Also I haven’t blogged for the longest time… Probably for the last 9 or 10 months. So we started of with a review about identities: cos2θ – sin2θ = 1 – 2sinθ 1 – sin2θ - sin2θ 1 – 2 sin2θ Q.E.D.

Quite a few points to take note of when writing down our answers were also given. One of them was to put your intermediate steps/ show more work so we can still get part marks in tests.

Later in we discuss the how identities are odd or even. SIN and TAN functions are ODD and COS functions are even.

sin(-θ) = - sin (θ) cos(-θ) = cosθ tan(-θ) = - tan (θ)

Mr. K gave us some pointers on how to do identities like doing the more complicated identities first, rewriting both sine and cosine and simplifying complex fractions. Then here goes the best part of class……

The SINE Dance

What is it for?? Its for remembering this:

sin(α [+/-] β) = (sin α )( cos β ) [+/-] ( cos α )( sin β )

cos(α [+/-] β) = (cos α )( cos β ) [+/-] ( sin α )( sin β )

The SINE DANCE for kinesthetic learning, where our body learns how to do things by repetitively doing or seeing it. Just like how we can dial a phone number with our fingers and not our hands, or how we know where our friends’ houses are without knowing their exact address.

If I feel like it I’ll try making a video on YouTube for the sine dance… Wanna join me Richard?? LOL…

Then we did some exercise:

The lesson was pretty much just having to do the proper evaluation of a function/ identities : sin = sin cos +/- cos sin and cos = cos cos + sin sin… After figuring out where those are it will be easy for us to continue…

Lastly we went through how to find α and β if only sine or cosine is given:

After being finding the sin β and the cos α, we can now answer the questions:

Now that we have found sin β and cos α, we can now solve the four equations that we were given in today’s class.

Find:

sin( α + β) sin( α – β) cos( α – β) cos (α + β)

This would just be the part with the simple math so I don’t think I need to show you guys this. We would just use the given data of sin α and cos β, and what we have for sin β and cos α, and plug them in for each of the equivalent values of the four problems.

REMEMBER: While solving for anything make sure that you have the brackets, especially when there are negative numbers and you're multiplying them.

To know what quadrants are answers are at we have to find the quadrants of the sine and cosine, compare them and voila… we have our answer

HAPPY PI DAY!!!

The next scribe would be….

g O t M e L k

Thanks for covering for me last Monday Sam…