Confusing Pre-Cal Study Guide Questions

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edd fedds

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Hi my name is Henryetta and I need help on the following Pre-Calculus Questions before 10:00 a.m. Friday Dec. 11th, 2009.I apologize if I come off rude. I'm not trying to rush, just really need help on these last few.Here are the questions:
1.)Use the coordinates for familiar angles on the unit circle to solve the equation sec(x)=-square root of 2, where pi<x<3pi/2?
a.x=4pi/3
b.x=pi/4
c.x=5pi/4
d.x=3pi/2
*I tryed to use cos-1(1/x)=(1/-square root of 2), and got 2.35 which was way off.

2.)The period of the function y=2sin(2x)-cos(3x) is?
a.4 pi
b.pi
c.2 pi
d.3 pi
*I tryed t=2pi/B=2pi/2=3.14 or pi {and/or} t=2pi/B=2pi/3-2=2pi/1=6.23 or 2pi. Which one is it?

3.) The domain of the funtion y=coslxl is?
a.(-1,1)
b.[-1,1]
c.(-infinity,0)
d.(-infinity, +infinity)
*I tryed to graph y=-cos(-x) and y=cos(x) and got x=0, x=1, x=-1 and chose a over choice d. Am I right?

4.)The function f(x)=3x+4sin(2x) appears periodic when graphed in the window [-4pi,4pi].
a.true
b.false
*Overall confused on how to start.

5.)A tower is supported by a guy wire from the top of the tower to the ground 16 ft from its base. The wire makes an angle of 62 degrees with the ground. The length of the wire is?
a.30.09 ft
b.18.12 ft
c.28.41 ft
d.34.08 ft
*I used SOH CAH TOA and chose CAH or cos=adj/hyp, and got 100/cos(62), then got lost.
*That's all. Please & Thank you so much. :mrgreen:
 
What have you tried? Where are you stuck?

Please be complete. Thank you! :wink:
 
1.)Use the coordinates for familiar angles on the unit circle to solve the equation sec(x)=-square root of 2, where pi<x<3pi/2?
a.x=4pi/3
b.x=pi/4
c.x=5pi/4
d.x=3pi/2
*I tryed to use cos-1(1/x)=(1/-square root of 2), and got 2.35 which was way off.

This is a "well-known" angle. If sec x = -?2, then cos x = -1/?2. This is true in the 2nd or 3rd quadrant. In this case, it is Quadrant III. In Q I, cos ?/4 = 1/?2, so in Q3 x = 5?/4.
C

2.)The period of the function y=2sin(2x)-cos(3x) is?
a.4 pi
b.pi
c.2 pi
d.3 pi
*I tryed t=2pi/B=2pi/2=3.14 or pi {and/or} t=2pi/B=2pi/3-2=2pi/1=6.23 or 2pi. Which one is it?

Looking at the graph, the period is 2?.

3.) The domain of the funtion y=coslxl is?
a.(-1,1)
b.[-1,1]
c.(-infinity,0)
d.(-infinity, +infinity)
*I tryed to graph y=-cos(-x) and y=cos(x) and got x=0, x=1, x=-1 and chose a over choice d. Am I right?

Assuming that the function is y = cos |x|, i.e. absolute value, d is the answer.

4.)The function f(x)=3x+4sin(2x) appears periodic when graphed in the window [-4pi,4pi].
a.true
b.false
*Overall confused on how to start.

If you graph it, you will see that it is symmetric to the origin, but not periodic.

5.)A tower is supported by a guy wire from the top of the tower to the ground 16 ft from its base. The wire makes an angle of 62 degrees with the ground. The length of the wire is?
a.30.09 ft
b.18.12 ft
c.28.41 ft
d.34.08 ft
*I used SOH CAH TOA and chose CAH or cos=adj/hyp, and got 100/cos(62), then got lost.

Why did you use 100?
cos 62° = 16/L
L = 16/cos 62° = 34.08087...
d
 
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