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 March 14th, 2011, 04:59 PM #1 Senior Member   Joined: Feb 2011 Posts: 118 Thanks: 0 Trigonometry Review Help!! Hey guys, I came across some confusing questions in my textbook that I need some solutions/help on if possible. 1) Let (xy) be a point other than the origin on the terminal side of an angle in standard position. Let r be the distance from the origin to (x,y). a) Match each term with its definition Sin (theta)=______ (r/y, r/x, x/r, x/y) Sec (theta)=______(r/y, r/x, x/r, x/y) Tan (theta)=_______(r/y, r/x, x/r, x/y) Cos (theta)=________(r/y, r/x, x/r, x/y) Cot (theta)=_______(r/y, r/x, x/r, x/y) csc (theta)=_______(r/y, r/x, x/r, x/y) b) Math the two lists Sec (theta)=_____((sin(theta)/cos(theta)), 1/tan(theta), 1/sin(theta), cos^2(theta)+sin^2(theta)) tan (theta)=______((sin(theta)/cos(theta)), 1/tan(theta), 1/sin(theta),cos^2(theta)+sin^2(theta)) 1=_______((sin(theta)/cos(theta)), 1/tan(theta), 1/sin(theta), cos^2(theta)+sin^2(theta)) csc (theta)=______((sin(theta)/cos(theta)), 1/tan(theta), 1/sin(theta),cos^2(theta)+sin^2(theta)) cot (theta)=_____((sin(theta)/cos(theta)), 1/tan(theta), 1/sin(theta), cos^2(theta)+sin^2(theta)) c) Math the two lists 1=_____(cos(3pi/2), tan180, sec(pi), cos(pi/2), tan(pi/2), csc pi, tan(3pi/2), sec(2pi) ) 0=_____(cos(3pi/2), tan180, sec(pi), cos(pi/2), tan(pi/2), csc pi, tan(3pi/2), sec(2pi) ) -1=______(cos(3pi/2), tan180, sec(pi), cos(pi/2), tan(pi/2), csc pi, tan(3pi/2), sec(2pi) ) undefined=______(cos(3pi/2), tan180, sec(pi), cos(pi/2), tan(pi/2), csc pi, tan(3pi/2), sec(2pi) ) I would appreciate some assistance on these questions, Thank you!!! p.s. If anything is unclear let me know.
 March 14th, 2011, 06:15 PM #2 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: Trigonometry Review Help!! Please see viewtopic.php?f=37&t=19563 I'll get you started though. Do you know "SOHCAHTOA" ?? If not, google that now. Then, make the following identifications: r = Hypothesis x = Adjacent y = Opposite.
 March 14th, 2011, 06:32 PM #3 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Trigonometry Review Help!! a) From the following, we can derive the answers: $x=r\cos\theta$ and $y=r\sin\theta$ thus: $\sin\theta=\frac{y}{r}$ $\sec\theta=\frac{1}{\cos\theta}=\frac{1}{$$\frac{x }{r}$$}=\frac{r}{x}$ $\tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{$$\ frac{y}{r}$$}{$$\frac{x}{r}$$}=\frac{y}{x}$ $\cos\theta=\frac{x}{r}$ $\cot\theta=\frac{\cos\theta}{\sin\theta}=\frac{$$\ frac{x}{r}$$}{$$\frac{y}{r}$$}=\frac{x}{y}$ $\csc\theta=\frac{1}{\sin\theta}=\frac{1}{$$\frac{y }{r}$$}=\frac{r}{y}$ b) $\sec\theta=\frac{1}{\cos\theta}$ $\tan\theta=\frac{\sin\theta}{\cos\theta}$ $1=\cos^2\theta+\sin^2\theta$ $\csc\theta=\frac{1}{\sin\theta}$ $\cot\theta=\frac{1}{\tan\theta}$ c) For these we can use (where k is an integer): $\sin$$0+k\pi$$=0$ $\sin$$\frac{\pi}{2}+2k\pi$$=1$ $\sin$$\frac{3\pi}{2}+2k\pi$$=-1$ $\cos$$0+2k\pi$$=1$ $\cos$$\frac{\pi}{2}+k\pi$$=0$ $\cos$$\pi+2k\pi$$=-1$ Now, we can answer the questions: $1=\sec$$2\pi$$=\frac{1}{\cos$$0+2(1)\pi$$}$    $-1=\sec$$\pi$$=\frac{1}{\cos$$\pi+(0)\pi$$}=\frac{1 }{-1}=-1$ $\text{undefined}=\tan$$\frac{\pi}{2}$$=\frac{\sin\ (\frac{\pi}{2}+2(0)\pi\)}{\cos$$\frac{\pi}{2}+(0)\ pi$$}=\frac{1}{0}$ $\text{undefined}=\csc$$\pi$$=\frac{1}{\sin$$0+(1)\ pi$$}=\frac{1}{0}$ $\text{undefined}=\tan$$\frac{3\pi}{2}$$=\frac{\sin $$\frac{3\pi}{2}+2(0)\pi$$}{\cos$$\frac{\pi}{2}+(1 )\pi$$}=\frac{-1}{0}$ Thanks from orangerify and lilili
March 14th, 2011, 06:35 PM   #4
Senior Member

Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,211
Thanks: 521

Math Focus: Calculus/ODEs
Re: Trigonometry Review Help!!

Quote:
 Originally Posted by The Chaz ... Do you know "SOHCAHTOA" ??...
We were taught "Oscar Had A Heap Of Apples."

Btw, If I hadn't already typed all that out above, I would've refrained from posting!

 March 14th, 2011, 07:32 PM #5 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: Trigonometry Review Help!! There you go, SPOILING the users again... I was hoping to see some of rule #(-4) surface!
 March 14th, 2011, 09:43 PM #6 Senior Member   Joined: Feb 2011 Posts: 118 Thanks: 0 Re: Trigonometry Review Help!! I'm learning through the shown solutions. I'm a visual learner to begin with, and seeing the solutions at hand, helps me proceed with other questions in the text. In the end of it all, this helps me through exams. So thank you!!
March 15th, 2011, 07:49 AM   #7
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Joined: Nov 2009

Posts: 67
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Re: Trigonometry Review Help!!

Quote:
 Originally Posted by The Chaz Please see viewtopic.php?f=37&t=19563 I'll get you started though. Do you know "SOHCAHTOA" ?? If not, google that now. Then, make the following identifications: r = Hypothesis [color=#FF0000]<======== I like that, The Chaz!! Revolutionary![/color] x = Adjacent y = Opposite.

 March 15th, 2011, 09:19 AM #8 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: Trigonometry Review Help!! What can I say? Q E D
 March 15th, 2011, 10:52 AM #9 Senior Member   Joined: Feb 2011 Posts: 118 Thanks: 0 Re: Trigonometry Review Help!! This forum alone is helping me get through my calculus course. So I appreciate whoever created such a site
March 15th, 2011, 10:58 AM   #10
Global Moderator

Joined: Nov 2009
From: Northwest Arkansas

Posts: 2,766
Thanks: 4

Re: Trigonometry Review Help!!

Quote:
 Originally Posted by ProJO This forum alone is helping me get through my calculus course. So I appreciate whoever created such a site
Sweet! I'm sure julien will be glad to hear of your gratitude.

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# Let (x,y) be a point other than the origin on the terminal side of an angle θ in standard position. Let r be the distance from the origin to (x,y).

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