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anonymous
 3 years 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
anonymous
 3 years 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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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Okay, let's make that drawing again, though following @hartnn 's advice, I'll do it properly this time ;) DRAW!!! dw:1360757734426:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Cosine is adj/hyp, right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So, we have cosθ = (5/9) We place the 5 and the 9, accordingly... dw:1360757883210:dw (Stop me when you don't understand)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Now, what's the length of this missing side... dw:1360758005338:dw (Hint: Pythagorean theorem)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\sqrt{106}\] right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Remember, 9 is your hypotenuse When you have a^2 + b^2 = c^2 9 is your c :)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\cos ^2(\theta)+\sin^2(\theta)=1\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\sin^2(\theta) = 1\cos^2(\theta)\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\sin^2(\theta)=(\frac{ 5 }{ 9 })^2 1\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i prefer the method provided by @PeterPan, because it shows you the inside out

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So, we can put sqrt(56) on here...dw:1360758287438:dw And you can easily get the other trig functions. Be careful though...

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes that is what i said

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i said i prefer the other method to know the inside out

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0we are allowed to draw on the test

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@savac REMEMBER THIS dw:1360758381571:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0although the identity was proven using pyth.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ACTS!!!! dw:1360758433801:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0savac PeterPan is doing a great job

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@mathsmind Thanks for the kudos! Much appreciated :)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So back to this... dw:1360758603756:dw Can you now determine the rest of the trig functions of this theta?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0:D I was about to say something clever, but you beat me to it :)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0REMEMBER In this particular quadrant, only sine (and cosecant) are positive

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0lol sorry running low on sleep

anonymous
 3 years 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/\[\sqrt{56}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0And there you have it :)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Well yeah, unless you want to make it \[\huge \sqrt{56}=2\sqrt{14}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0wow i surprised myself. lol thank you very much

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Just 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0thats what i thought it was

hartnn
 3 years 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Looks more complicated.

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

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

hartnn
 3 years 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.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Identities are harder to swallow, and they taste kinda awful too :(
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