Tuesday

March 3, 2015

March 3, 2015

Posted by **mysterychicken** on Thursday, June 6, 2013 at 2:52pm.

1. Solve sin2xcos2x = 4sin2x on the interval [0, 2pi]

0, pi, 2pi?

2. Exact value of sin(pi/12) - sin(5pi/12)

root3/4?

3. Using factorial notation, 0! = 1

False?

4. Find the area of the following triangle. a=4.8inches, b=6.3inches, c=7.5inches. Round answer to nearest tenth

- math -
**mysterychicken**, Thursday, June 6, 2013 at 2:54pmarea is 1/2bh...so can I make any side the base/height?

- math -
**Steve**, Thursday, June 6, 2013 at 3:53pm#1

sin2xcos2x = 4sin2x

sin2x(cos2x-4) = 0

sin2x = 0 or cos2x = 4

so, 2x = 0,π,2π,3π,4π

x = 0,π/2,π,3π/2,2π

naturally, cos2x=4 has no solutions.

Again, you found solutions for__2x__in [0,2π], but you want all values for**x in [0,2π]**

#2 Since sin u − sin v = 2 sin(½(u−v)) cos(½(u+v)),

sin(pi/12) - sin(5pi/12)

Using the half-angle formula,

= √((1 - cos pi/6)/2)-√((1 + cos pi/6)/2)

= 1/√2 (√(1-√3/2)-√(1+√3/2))

= 1/√2 (√((2-√3)/2) - √((2+√3)/2))

= 1/√2 (1/2) (√(4-2√3)-√(4+2√3))

= 1/2√2 ((√3-1)-(√3+1))

= 1/2√2 (-2)

= -1/√2

Or, using the sum/difference formulas,

sin u − sin v = 2 sin(½(u−v)) cos(½(u+v))

sin(pi/12) - sin(5pi/12)

2sin(-pi/6)cos(pi/4)

= 2(-1/2)(1/√2)

= -1/√2

#3 True. It is defined that way.

4. yes, any side can be the base.

so how do you get the height?

You might consider Heron's formula.

- math -
**mysterychicken**, Thursday, June 6, 2013 at 3:59pmI asked my teacher for answer choices for #2 and she said -root2/2, root2/2, or -root3/4...

you said -1root2

- math -
**Steve**, Thursday, June 6, 2013 at 4:23pmas you surely know by now

1/√2 = 1/√2 * √2/√2 = √2/2

c'mon, man.

- math -
**mysterychicken**, Thursday, June 6, 2013 at 4:49pmGotcha!

- math -
**mysterychicken**, Thursday, June 6, 2013 at 5:00pmI get 15.03 for the area...is that correct?

- math -
**Steve**, Thursday, June 6, 2013 at 5:11pmLooks good to me.

Did you crank that out manually? I wen to

wolframalpha.com and typed in

√(s(s-a)(s-b)(s-c)) where a=4.8 and b=6.3 and c=7.5 and s=(a+b+c)/2

- math -
**mysterychicken**, Thursday, June 6, 2013 at 5:21pmYes I got the formula and plugged the values in :)

**Answer this Question**

**Related Questions**

Math - Can I please get some help on these questions: 1. How many solutions does...

math-PLEASE CHECK - Find the surface area and volume of each of the following ...

trig - determine the solutions for tanxcos^2x-tanx=0 in the interval XE[-2pi,2pi...

algebra - i need someone to explain to me how i got this answer...i know the ...

Precal - How do you find all the polar coordinates of P=(-1, -2pi/3)? I've read ...

Calculus AP - Volume of Revolution - Hi. I have a few calculus problems that I ...

College Pre-Algegra - 1. Find the exact value of tan660 using the functions of ...

PreCalculus - Hi I need some assistance on this problem find the exact value do ...

trig - Solve cos x-1 = sin^2 x Find all solutions on the interval [0,2pi) a. x=...

Calc - find absolute max and min of f(x)=cosx+sin^2(x) on interval [0,2pi]. Give...