Trigonometric function, problem with finding X in regards to somenumber

J

junkwisch

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Mar 30, 2013
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Hi, I got stuck in some questions on my textbook. I'm totally clueless so I decide to ask you guy about it.

In exercise 7-12, one of sin x, cos x and tan x is given. Find the other two if x lies in the specified interval.

7. Sin(x)=3/5, X E [pi/2,pi] (how do you insert symbol for pi?)

I don't really know how to do this question, because I don't know how to find the value of X, when is it equal to 3/5 (calculator not allowed), can you guy tell me how to find X?


Another question

12. Sin (x) = -1/2 ,X E [pi, 3pi/2]
I'm not sure if this is correct or not, but my guess is that X is equal to 7pi/6
thus Cos (7pi/6) = -root3/2 (again how do you make a root symbol) since Cos(x) is negative in third quotient
and Tan (7pi/6) = 1/root3 since tan(x) is positive in third quotient

Is this is correct? if not please tell me what I did wrong.

Thank you
Pat
 
For the first one: You don't need the value of x. Translating into plain language, sin(x) = 3/5 means that x is an acute angle in the right-triangle whose opposite side is length 3 and hypotenuse is length 5. You will need to use the Pythagorean theorem to find the side adjacent to x. Once you have this you can find all six trigonometric values of x. Note that x lies in quadrant 2, so the cosine and tangent will be negative.

For your second one, you are correct, though I'm a little confused as to your method of "guess."
 
I have another question to ask, but this one is about vector

so if the question is like

V=(5,6) in R^2, there are two units of vector U1,U2 in R^2 which are perpendicular to v. Find their coordinates.


I really have no idea how to figure out this question, can any one tell me how to solve question like this?

thankyou
 
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