Hi I have a few problems that I need some help on:

1. Find the point (x,y) on the unit circle that corresponds to the real number t = 4pi/3

2. Given sin data = -2/9 and tan data > 0, find cos data.

3. Find the reference angle for data = -155

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- Feb 12th 2008, 08:30 PMHe is legendHi, need help on some trig funct. problems
Hi I have a few problems that I need some help on:

1. Find the point (x,y) on the unit circle that corresponds to the real number t = 4pi/3

2. Given sin data = -2/9 and tan data > 0, find cos data.

3. Find the reference angle for data = -155 - Feb 12th 2008, 08:52 PMJhevon
imagine you draw a this angle and it cuts the unit circle at a point. you can draw a right angled triangle with this point, the base of which lies on the x-axis. it will be in the 3rd quadrant, with the angle pi/3 between the angle and the negative x-axis. the hypotenuse will be 1 (the radius of the unit circle).

using trig ratios:

the height of the triangle (the y-value you are looking for) is given by: - sin(pi/3)

the base (the x-value you are searching for) is given by: cos(pi/3)

Quote:

2. Given sin data = -2/9 and tan data > 0, find cos data.

note that we are in the third quadrant, since sine is negative and tangent is positive. thus, we must have a negative value for cosine as well.

there are two ways to do this: by formula, or by trig/geometry

by formula: note that $\displaystyle \cos^2 \theta = 1 - \sin^2 \theta$

so, $\displaystyle \cos \theta = \pm \sqrt{1 - \sin^2 \theta}$

as i said, here we want $\displaystyle \cos \theta = {\color{red} - }~ \sqrt{1 - \sin^2 \theta}$

just plug in the value for the sine and simplify

by trig/geometry. draw a right triangle. call an acute angle in the triangle $\displaystyle \theta$. since sine of this angle is 2/9 (*), label the side opposite this angle 2 and label the hypotenuse 9. you can find the adjacent side by using Pythagoras' theorem. then you know cosine = adjacent/hypotenuse (and remember to put the minus sign at the end because we are in the third quadrant).

Quote:

3. Find the reference angle for data = -155

write the angle as a positive one.

$\displaystyle -155^o = -155^o + 360^o = 205^o$

this angle is between 180 and 270. when $\displaystyle 180 < \theta < 270$, the reference angle for $\displaystyle \theta$ is given by: $\displaystyle \theta - 180$. since we want the angle between $\displaystyle \theta$ and the x-axis

*) i am considering positive numbers here, we'll worry about negatives at the end. since we know what quadrant the angle is in, we know to apply a negative sign to the answer we get