Can someone please check my answers!
2. Find value of cos(255degrees)cos(105degrees)
root3 - 2 / 4
3. cos(pi/12) - cos(5pi/12)
Is it root3/4?
4. Use the appropriate sum-to-product formula to rewrite the expression sin6x - sin9x
I don't really understand how to do these, but I got -2sin(3x/2)cos(15x/2)..
5. same type of question: rewrite the expression cos4x - cos3x
Is it cosx??
on all these, they are the same thing. I am not certain how you see 4,5 as different.
look here: http://www.sosmath.com/trig/Trig5/trig5/trig5.html Print that out. Notice the sum to product formulas. If you were my student, I would have you write each formula on a flash card until you memorized it.
work on using those formulas on that page.
Okay, I understand 4 and 5. But what about 2 and 3?
Nevermind, I get it
check my solutions for #1, and #2
http://www.jiskha.com/display.cgi?id=1370293791
3. CosA-cosB= -2(sin((a+b)/2)*sin((a-b)/2)
THEN
COS(pi/12) - cos(5pi/12)
= -2(sin( SUM/2)*sin(DIFF/2)
= -2(SIN 6pi/24 *SIN(-4pi/24))
= -2 SIN pi/4 * SIN -pi/6)
= 2SIN (45)* SIN30
= SQRT2*1/2=.707
2/ USE THE FORMULA
COSa*COSb= 1/2 (COS(A-B)+COS(a+B) )
Sure, I can help you check your answers and explain how to get them!
2. Find value of cos(255 degrees)cos(105 degrees):
To find the value of cos(255 degrees)cos(105 degrees), you can use the product-to-sum identity, which states that cos(A)cos(B) = (1/2)[cos(A + B) + cos(A - B)]. Let's apply this formula:
cos(255 degrees)cos(105 degrees) = (1/2)[cos(255 + 105) + cos(255 - 105)]
= (1/2)[cos(360) + cos(150)]
= (1/2)[cos(150)]
= (1/2)[-√3/2]
= -√3/4
Therefore, the value of cos(255 degrees)cos(105 degrees) is -√3/4.
3. Find cos(pi/12) - cos(5pi/12):
To evaluate cos(pi/12) - cos(5pi/12), we can use the difference-to-product identity, which states that cos(A) - cos(B) = -2sin[(A + B) / 2] sin[(A - B) / 2]. Let's apply this formula:
cos(pi/12) - cos(5pi/12) = -2sin[(pi/12 + 5pi/12) / 2] sin[(pi/12 - 5pi/12) / 2]
= -2sin[2pi/12] sin[-2pi/12]
= -2sin(pi/6) sin(-pi/6)
= -2(1/2)(-1/2)
= 1/2
Therefore, cos(pi/12) - cos(5pi/12) equals 1/2.
4. Use the appropriate sum-to-product formula to rewrite sin(6x) - sin(9x):
To rewrite sin(6x) - sin(9x) using the sum-to-product identity, we can use the formula sin(A) - sin(B) = 2cos[(A + B) / 2] sin[(A - B) / 2]. Let's apply this formula:
sin(6x) - sin(9x) = 2cos[(6x + 9x) / 2] sin[(6x - 9x) / 2]
= 2cos(15x/2) sin(-3x/2)
= -2cos(15x/2) sin(3x/2)
Therefore, sin(6x) - sin(9x) can be rewritten as -2cos(15x/2) sin(3x/2).
5. Rewrite the expression cos(4x) - cos(3x):
To rewrite cos(4x) - cos(3x), we can use the sum-to-product identity, which states that cos(A) - cos(B) = -2sin[(A + B) / 2]sin[(A - B) / 2]. Let's apply this formula:
cos(4x) - cos(3x) = -2sin[(4x + 3x) / 2]sin[(4x - 3x) / 2]
= -2sin(7x/2)sin(x/2)
Therefore, the expression cos(4x) - cos(3x) can be rewritten as -2sin(7x/2)sin(x/2). It is not just equal to cos(x).