ok I appologize for my stupidity...
I'll answer your question...
ok instructions to this problem
In problems 77-88, use properties of the trigonmetric functions to find the exact value of each expression. Do not use a calculator
85. sin(-pi/12)csc( (25 pi)/12 )
book dosen't say weather or not if it's in radians but I assume it is...
Ok I just put it into my calculator and got negative one I'm in radian mode...
Here's what I put in my calculator...
(sin(-pi/12))/(sin((25pi)/12))
My back of the book, sense this is an odd problem gives me also -1 here's why...
when you added pi to the denomenator you forgot to make it negative...
this would give you negative one
ok
I have a question
why is sin(-20)/cos 380
= to tan of -200
I know sin over cos is tan just don't see were the -200 came from thanks!
see...
(- sin pi/12 + pi)/(sin (25 pi)/12 + pi)
this becomes
(sin pi/12 + pi)/(-sin (25 pi)/12 + pi)
finish it off and you get negative one...
why is sin(-20)/cos(380) equal to tan(-200)
I don't understand
No need to apologize, we're here to help! Let's break down your question and explain how to get the answer.
To understand why sin(-20) / cos(380) is equal to tan(-200), we need to review the properties of trigonometric functions.
1. First, let's convert the angles to their equivalent angles within one full revolution (360 degrees or 2π radians).
-20 degrees is equivalent to 360 - 20 = 340 degrees.
380 degrees is equivalent to 380 - 360 = 20 degrees.
You mentioned radians, so let's convert these degrees to radians.
340 degrees is equivalent to 340 * π / 180 = 17π / 9 radians.
20 degrees is equivalent to 20 * π / 180 = π / 9 radians.
2. The angle values we have are now -20 degrees and 380 degrees (or π / 9 and 17π / 9 in radians).
3. Now, let's look at the relationship between the trigonometric functions: sin, cos, and tan.
The definition of the tangent function (tan θ) is sin θ / cos θ.
4. In this case, sin(-20) / cos(380) can be simplified as follows:
- sin(-20) can be rewritten as -sin(340) because -20 degrees is equivalent to 340 degrees.
- cos(380) can be rewritten as cos(20) because 380 degrees is equivalent to 20 degrees.
5. Using our conversion values, we find that -sin(340) / cos(20) is equal to tan(-200), which is the same as saying tan(160).
Therefore, sin(-20) / cos(380) is equal to tan(-200) or tan(160).
In summary, the angle values were equivalent due to the periodic nature of trigonometric functions. By converting the angles to their equivalent values within one full revolution and applying the definition of tangent, we find that sin(-20) / cos(380) is equal to tan(-200) (or tan(160)).