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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
 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
 one year ago

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

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

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

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

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

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

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

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

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

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

PeterPanBest 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
 one year ago

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

PeterPanBest ResponseYou've already chosen the best response.2
Just 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
 one year ago

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

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

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

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

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

hartnnBest ResponseYou've already chosen the best response.0
if 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.
 one year ago

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