Trigonomic Functions Help: simplify expressions, using identities

[nbg273]

Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula:

A) sin 4(degrees)
-----------------
1+cos 4(degrees)


B) 1-cos 6(theta)
-----------------
sin 6(theta)

I'm starting Calculus but had a terrible Pre-Calc. teacher, so I have to learn almost everything over again and I don't understand these questions... Please help me understand...

Thank you.

 

[ksdhart2]

I think a good place to begin would be to brush up on the double angle identities and half angle identities. The website Purple Math has a page with many trigonometric identities, including the double angle and half angle identities. Looking at that list, I see one identity which looks like both of your problem. Can you see which one it is? What happens if you try to apply that identity? Note that if you let $\displaystyle x=4^{\circ}$, then $\displaystyle 2x=8^{\circ}$ and $\displaystyle \dfrac{x}{2}=2^{\circ}$. Please share with us any and all work you've done on these problems, even the parts you know are wrong. Thank you.

 

[stapel]

Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula:

\(\displaystyle \mbox{A) }\, \dfrac{\sin(4^{\circ})}{1\, +\, \cos(4^{\circ})}\)

\(\displaystyle \mbox{B) }\, \dfrac{1\, -\, \cos(6\theta)}{\sin(6\theta)}\)

Are the above a correct interpretation of what you meant? Also, are you sure the instructions specified to use double- and half-angle identities for both of these exercises?

Thank you!

 

[nbg273]

Are the above a correct interpretation of what you meant? Also, are you sure the instructions specified to use double- and half-angle identities for both of these exercises?

Thank you!

Yes, those are correct. I'm sorry, I don't know how to use this site. And yes, it specified to use one or the other of those formulas.

 

[Otis]

I don't know how to use this site.

You don't need to use the LaTex code, to format mathematical expressions. You can type your expressions by using grouping symbols around numerators and denominators, with function notation.

[sin(4 deg)] / [1 + cos(4 deg)]

[1 - cos(6*theta)] / [sin(6*theta)]

And yes, it specified to use one or the other of those formulas.

Do you have a list of trig identities? (Note that Wikipedia does not use function notation, on that page.)

Look at the half-angle formulas for sine, cosine, and tangent.

Do you see anything that matches the first expression above?

For the second expression, try some formulas, and see what simplifications you come up with.

If you would like more help, please show us what you tried.

 

[Deleted member 4993]

Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula:

A) sin 4(degrees)
-----------------
1+cos 4(degrees)


B) 1-cos 6(theta)
-----------------
sin 6(theta)

I'm starting Calculus but had a terrible Pre-Calc. teacher, so I have to learn almost everything over again and I don't understand these questions... Please help me understand...

Thank you.

Hint:

4° = 2 * (2°)

6Θ = 2 * (3Θ)