<ol>
<li><p>Cos (2pi - X) =?
a. sin x
b. -sin x
c. cos x
d. -cos x
e. tan x
The answer is C. I remember learning this in trig, but I forgot how to solve this.</p></li>
<li><p>Solve the equation on the interval [0,2pi)Cos 2x =sqrt{2}/2
a. pi/4, 3pi/4, 5pi/4, 7pi/4
b. pi/8, 7pi/8. 9pi/8, 15pi/8
c. all the above
e. no solution </p></li>
</ol>
<p>the answer is B. I looked on the unit circle and found when X=sqrt{2}/2, then I put that value in radians and divided by two. That method only worked for two of the four answers in b, so I am concerned that, that method was incorrect.</p>
<p>1) 2pi on the unit circle is one entire revolution, meaning the question is really cos(-x). Cosine is an even function, meaning cos(-x)=cos(x), therefore it’s C
2) To solve this, you start off just as you did; replace 2x with another variable, y. cos(y) = (root2)/2. Then take the inverse cos of of (root2)/2, leaving you with pi/4 and 7pi/4. But because the original cosine was of 2x, the graph will wrap around the unit circle twice, meaning the solutions are
y = pi/4, 7pi/4, pi/4 +pi, 7pi/4 +pi
x = pi/8, 7pi/8, pi/8 + 8pi/8, and 7pi/8 + 8pi/8, otherwise known as (b. pi/8, 7pi/8. 9pi/8, 15pi/8 )</p>
<p>Thanks! </p>
<p>btw is Sin (-x)=sin(x) and tan(-x)=-tan(x)?</p>
<p>@pokemonfan</p>
<p>Sin (-x) = -Sin (x)
Tan (-x) = -tan (x)</p>
<p>Nope. Sin(-x) = -sin(x) and
Tan(-x) = sin(-x)/cos(-x) = -sin(x)/cos(x) = -tan(x)</p>
<p>I kind of still don’t get the concept for number 1.</p>
<p>If the question was cos ((2pi/3) - x) = ?
would it mean that because that quadrant 2, it would be negative, thus, cos(-X), so the answer would be “cos x”?</p>
<p>or </p>
<p>cos ((2pi/3) - x) = sin(2pi/3)cos(y) - cos(2pi/3)sin(y)
sin 2pi/3 = sqrt(3)/2 and cos 2pi/3 = -1/2
this gives:
cos (2pi/3 - x) = -cos x - 0 = -cos x</p>
<p>Unfortunately, cos(2pi/3-x)=? can not be solved the same way. 2pi is special in trig in the sense that it represents a full rotation. Adding 2pi to the argument of a trig function does not change its value, which is why cos(2pi-x)=cos(-x+2pi)=cos(-x). For most other angles we would have to use the angle addition formula for cos, namely that cos(a+b)=cos(a)cos(b)-sin(a)sin(b). (you used the wrong formula for addition, confusing the sine and cosine formulas)</p>