Finding exact values of trig expressions. Without calculator

[kowens]

1. sin(240-315) <<this is in degrees.

2. cos105 <<also in degrees.

I have no clue how to work these. Any help would be appreciated.

 

[DrSteve]

Re: Finding exact values of trig expressions. Without calcul

For the first one you want to use the identity sin(A-B) = sin A cos B - cos A sin B.

You will want to do something similar for the second one, but you need to replace the given number by a sum or difference of "easier" numbers first.

I hope this gets you started. Let me know if you need more hints.

 

[mmm4444bot]

A different approach to part (1) is to first do the arithmetic inside the parentheses.

sin(240° - 315°) = sin(-75°)

75° is the reference angle for -75°

This changes the exercise to finding -sin(75°) because sine is negative in Quadrant IV.

Since 75 is the same as 30 + 45, and since 30° and 45° are both special angles for which we have already memorized the sine and cosine values, we can readily find the answer using another common identity:

sin(30° + 45°) = sin(30°) cos(45°) + cos(30°) sin(45°)

Multiply the result by -1, to finish.

 

[kowens]

Re: Finding exact values of trig expressions. Without calcul

i need more hints.

 

[Deleted member 4993]

Re: Finding exact values of trig expressions. Without calcul

i need more hints.

stuck.

Show us what have you done with the hints and exactly where you are

 

[DrSteve]

Re: Finding exact values of trig expressions. Without calcul

\(\displaystyle \cos 105 = \cos(60+45) = \cos 60 \cos 45 - \sin 60 \sin 45 = (\frac{1}{2})(\frac{\sqrt{2}}{2})+(\frac{\sqrt{3}}{2})(\frac{\sqrt{2}}{2})\)

 

[mmm4444bot]

i need more hints.

I'm not convinced.

I think that it would be better for you to start asking specific questions, instead.

What exactly is it that confuses you in your lessons?

I mean, pick one thing, and tell us what it is.

At this point, we've nearly completed your exercises for you.