A community for students.
Here's the question you clicked on:
 0 viewing
savac
 2 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
savac
 2 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

This Question is Closed

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

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

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

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

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

PeterPan
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.2yes that is what i said

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

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

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

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

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

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

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

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

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

savac
 2 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/\[\sqrt{56}\]

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

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

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

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

hartnn
 2 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

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

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

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

hartnn
 2 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.

PeterPan
 2 years ago
Best ResponseYou've already chosen the best response.2Identities are harder to swallow, and they taste kinda awful too :(
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.