GOODMAN
Suppose (theta sign) is an angle in standard position whose terminal side lies in the given quadrant. For these functions, find the exact values of the remaining five trigonometric funtctions of (theta)
sin(theta)=-4/5; Quadrant 4
tan(theta)=2; Quadrant 1
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imranmeah91
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sin(theta)=-4/5
|dw:1335488862320:dw|
imranmeah91
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|dw:1335488894071:dw|
GOODMAN
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How did you get that triangle?
imranmeah91
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I drew a triangle and use the fact the sin (theta)=-4/5
remember sine is opposite over hypothenuse
GOODMAN
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Ohhh, thats how you did it, okay!
GOODMAN
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Now the 5 trig funtions of theta? I thought there were 3 trig functions o.O
imranmeah91
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now let's find adjacent side value using pythagorean theorem
a^2+4^2=5^2
a^2=25-16
a^2=9
a=3
imranmeah91
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|dw:1335489127010:dw|
imranmeah91
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now we can see what cos , and tan are
cos is adjacent over hypotenuse
cos(theta)= 3/5
imranmeah91
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Tangent is sin(theta)/cos(theta)
-4/5
------ =-4/3
3/5
GOODMAN
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Okay, i got those two, what are the other 3 they are looking for?
imranmeah91
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csc(theta)= 1/sin(theta)= 1 = -5/4
-----
-4/5
imranmeah91
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sec(theta)= 1/cos(theta)= 1/ (3/5) = 5/3
imranmeah91
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cot(theta)= 1/tan(theta)= 1/(-4/3) =-3/4
GOODMAN
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Oh we use the recriprocoals
imranmeah91
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yep
GOODMAN
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Ooooo, that makes much more sense!!! Okay, i know how to do the fraction one as we did now, but what about the second one, tan(theta)=2..how do i set that up?
imranmeah91
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tan(theta)=2=2/1; Quadrant 1
|dw:1335489526582:dw|
imranmeah91
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use pythagorean theorem to find hypotenuse
GOODMAN
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Okay, so basically, if its a whole number, we put it as a fraction?
imranmeah91
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yes
GOODMAN
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Hypotenuse is square root of 3
imranmeah91
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sqrt[2^2+1^2]=sqrt[5]
GOODMAN
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Srry, did it in my head, got my trusy calculator :D
GOODMAN
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Okay, i got it, thanks for helpin :D
imranmeah91
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anything for my shrink
GOODMAN
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LOL, i might just pass algebra 2
imranmeah91
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I took algebra 2 in sophomore year, and it was big deal way back
GOODMAN
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Im taking it freshman :p
imranmeah91
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smartie
GOODMAN
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I wish, lol, i just barely pass every time.
imranmeah91
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pre calc next year and then calculus
GOODMAN
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arghhh..dont remind me :/ Im taking summer school to prep for it.