Solve cos315*cos(-390)-sin225*sin750
cos315:
<RA = 360-315
= 45
cos45 = 1/√2
cos-390:
<RA=-390+360
=30
cos30= √3/2
sin225:
<RA = 225-180
= 45
Sin45=1/√2
Sin750:
<RA = 750 - 2(360)
=30
Sin30=1/2
Put it all together...
(1/√2)(√3/2)-(1/√2)(1/2)
=√3/2√2 - 1/2√2
The answer in the back is √2 + √6/4...
What did I do wrong?
sin225 is in the third quadrant, sine is negative.
cos-390 is in the fourth quadrant, positive.
change that sign, you get it (after rationalizing the denominator)
Thanks^
It seems like there might be a mix-up with the calculations. Let's go through the steps again to find out where the mistake occurred.
First, let's calculate cos315:
cos315 = cos(360 - 315) = cos(45) = 1/√2
Next, let's calculate cos(-390):
cos(-390) = cos(-390 + 360) = cos(-30) = √3/2
Moving on to sin225:
sin225 = sin(225 - 180) = sin(45) = 1/√2
Lastly, let's calculate sin750:
sin750 = sin(750 - 2(360)) = sin(30) = 1/2
Now, putting it all together:
cos315 * cos(-390) - sin225 * sin750
= (1/√2) * (√3/2) - (1/√2) * (1/2)
= (√3/2√2) - (1/2√2)
= (√3 - 1)/2√2
Therefore, the correct answer is (√3 - 1)/2√2, which is not the same as √2 + √6/4. It seems like the discrepancy might be due to an error in the calculations provided in the answer key.