Thread: a couple tricky trig function problems

1. a couple tricky trig function problems

1) express as a sum or difference as it applies to: sin(5x)sin(3x)

2) find the exact value in radical form for: cos(45)cos(15)

I'm not sure if I'm supposed to put two questions in one thread, but i thought that maybe they were worked similarly so I could lump them together. Also, the integers in problem two are in degrees, not radians. And I think that I'm supposed to use identities to solve these but I'm not sure which one.

2. Originally Posted by GUNSLINGAZ
1) express as a sum or difference as it applies to: sin(5x)sin(3x)

2) find the exact value in radical form for: cos(45)cos(15)

I'm not sure if I'm supposed to put two questions in one thread, but i thought that maybe they were worked similarly so I could lump them together. Also, the integers in problem two are in degrees, not radians. And I think that I'm supposed to use identities to solve these but I'm not sure which one.

For Q1, you should have a formula somewhere which gives an expression for sin A x sin B. Find that first then sub in 5x for A and 3x for B.

For Q2, use a similar expression for cos A x cos B, sub in appropriate values and then simplify.

You should know sin, cos, tan of 30, 45 and 60 off by heart.

If you don't, I suggest you do this:

Draw an equilateral triangle - let each side be length 2 - slice it down the middle - you now have a 30, 60, 90 triangle with the hypotenuse 2, base 1 - use Pythagoras to work out the other side is sqrt(3) - mark in your angles. You can then read off sin, cos, tan of 30 and 60 degrees.

For 45 degrees, draw a right-angled isoceles triangle with side lengths and (by Pythagoras) hypotenuse is sqrt(2). Label angles - read off sin, cos tan of 45 degrees.

3. Originally Posted by GUNSLINGAZ
1) express as a sum or difference as it applies to: sin(5x)sin(3x)

2) find the exact value in radical form for: cos(45)cos(15)

I'm not sure if I'm supposed to put two questions in one thread, but i thought that maybe they were worked similarly so I could lump them together. Also, the integers in problem two are in degrees, not radians. And I think that I'm supposed to use identities to solve these but I'm not sure which one.

hi

in general ,

sin A sin B = -(1/2)[cos (A+B)-cos (A-B)]

cos A cos B=(1/2)[cos (A+B)+cos (A-B)]

4. thanks so much. in looking at my handout, i know see the identities you mention under "product to sum identities." thanks.

5. find the exact value in radical form for: cos(45)cos(15)
$\displaystyle cos(a-b) = cosacosb+sinasinb$
= cos(45)*(cos(45-30))
= cos(45)*(cos45cos30+sin45sin30)
rest is numerical