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 one year ago
Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle.
cos θ = − 5/9, sin θ > 0
 one year ago
Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle. cos θ = − 5/9, sin θ > 0

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PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2Okay, let's make that drawing again, though following @hartnn 's advice, I'll do it properly this time ;) DRAW!!! dw:1360757734426:dw

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2Cosine is adj/hyp, right?

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2So, we have cosθ = (5/9) We place the 5 and the 9, accordingly... dw:1360757883210:dw (Stop me when you don't understand)

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2Now, what's the length of this missing side... dw:1360758005338:dw (Hint: Pythagorean theorem)

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2Remember, 9 is your hypotenuse When you have a^2 + b^2 = c^2 9 is your c :)

mathsmind
 one year ago
Best ResponseYou've already chosen the best response.2\[\cos ^2(\theta)+\sin^2(\theta)=1\]

mathsmind
 one year ago
Best ResponseYou've already chosen the best response.2\[\sin^2(\theta) = 1\cos^2(\theta)\]

mathsmind
 one year ago
Best ResponseYou've already chosen the best response.2\[\sin^2(\theta)=(\frac{ 5 }{ 9 })^2 1\]

mathsmind
 one year ago
Best ResponseYou've already chosen the best response.2i prefer the method provided by @PeterPan, because it shows you the inside out

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2So, we can put sqrt(56) on here...dw:1360758287438:dw And you can easily get the other trig functions. Be careful though...

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2@mathsmind You do need to do this to illustrate the pythagorean identities you posted. Though if you're not allowed to draw, better know the pythagorean (and other) identities by heart!!! :D

mathsmind
 one year ago
Best ResponseYou've already chosen the best response.2yes that is what i said

mathsmind
 one year ago
Best ResponseYou've already chosen the best response.2i said i prefer the other method to know the inside out

savac
 one year ago
Best ResponseYou've already chosen the best response.0we are allowed to draw on the test

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2@savac REMEMBER THIS dw:1360758381571:dw

mathsmind
 one year ago
Best ResponseYou've already chosen the best response.2although the identity was proven using pyth.

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2ACTS!!!! dw:1360758433801:dw

mathsmind
 one year ago
Best ResponseYou've already chosen the best response.2savac PeterPan is doing a great job

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2@mathsmind Thanks for the kudos! Much appreciated :)

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2So back to this... dw:1360758603756:dw Can you now determine the rest of the trig functions of this theta?

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2:D I was about to say something clever, but you beat me to it :)

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2REMEMBER In this particular quadrant, only sine (and cosecant) are positive

savac
 one year ago
Best ResponseYou've already chosen the best response.0lol sorry running low on sleep

savac
 one year ago
Best ResponseYou've already chosen the best response.0ok i got sin=\[\sqrt{56}\]/9 tan=\[\sqrt{56}\]/5 csc=9/\[\sqrt{56}\] sec=9/5 cot=5/\[\sqrt{56}\]

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2And there you have it :)

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2Well yeah, unless you want to make it \[\huge \sqrt{56}=2\sqrt{14}\]

savac
 one year ago
Best ResponseYou've already chosen the best response.0wow i surprised myself. lol thank you very much

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2Just place that right triangle in the correct quadrant, and you can't go wrong :) You'll notice that the horizontal bit was to the left of the xaxis, so strictly speaking, that's a 5, not a 5 :D

savac
 one year ago
Best ResponseYou've already chosen the best response.0thats what i thought it was

hartnn
 one year ago
Best ResponseYou've already chosen the best response.0actually since theta is in 2nd quadrant, that is its measure is between 90 to 180, the triangle will be , dw:1360722028091:dw

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2Looks more complicated.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.0but the way its solved and answers are correct.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.0sin and cosec will be positive, all other ratios will be negative.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.0if you want to solve using diagram, then what i have drawn must be used . here, its solved using identities, which is altogether different method and doesn't need drawing triangle.

PeterPan
 one year ago
Best ResponseYou've already chosen the best response.2Identities are harder to swallow, and they taste kinda awful too :(
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