Sin cos problem finding exact value

1. Jan 9, 2005

aisha

sin cos problem finding exact value....

I have to find the exact value of : $$\frac {\sin^2 45 degrees + \cos ^2 45 degrees} {\sin 60 degrees \cos 30 degrees}$$

The squares are throwing me off , without them I got
$$\frac {\frac {1} {sqrt2} + \frac {1} {sqrt2}} {3/2}$$

what do I do with the sqares on sin and cos in the numerator?

Last edited: Jan 9, 2005
2. Jan 9, 2005

Try this:

$$sin^2 45 degrees [tex], Sin(45) = radical 2 / 2, so sin^2(45) = 2/4 3. Jan 9, 2005 dextercioby If u use these formulas [tex] \sin^{2}x+\cos^{2}x=1$$
,for all "x"
and
$$\sin(90-x)=\cos x$$
,u'd have the problem solved.

Besides,your calculations are wrong,since at the numerator they didn't include squaring thevalues for sine and cosine,which were supposed to be done.

And the denominator is 3/4.

Daniel.

4. Jan 9, 2005

aisha

ok without the square roots on the sine and cosine I get 2/3 but the solution says the answer is 4/3?

5. Jan 9, 2005

dextercioby

If the denominator is 3/4 and the numerator is 1,what is the whole fraction equal to??

Daniel.

6. Jan 9, 2005

aisha

$$\sin 60 = \frac {sqrt3} {2}$$

and doesnt $$\cos 30 = \frac {sqrt3} {2}$$ also?

these multiplied gives 3/2 ??

How do u get the denominator to equal 3/4?

7. Jan 9, 2005

dextercioby

The multiplication is wrong.U multiplied only the numerators.U need to multiply the denominators as well.I'm sure you'll get
$$2\cdot 2 =4$$

Daniel.

8. Jan 9, 2005

thursdaytbs

(sqrt3/2) * (sqrt3/2) = 3/4

you forgot to multiply the two TWO's.

I've done that before, =\.

9. Jan 9, 2005

aisha

LOL omg silly me :rofl: Thanks Holy cant believe I missed that thanks