How to determine the sign of cos

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Loki123

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I need to determine cos a, tan a and cot a if I know sin a = 5/13 with a being from pi/4 to pi... I know how to determine cos, tan and cot, but I don't know how to determine is cos is positive or negative due to alpha's interval... What do I do?
IMG_20220123_174138.jpg
 
With the given interval and the given ratio, you may have two sets of answers that you need to report: one for values in the 1st quad., and one for values in the 2nd quad.
 
R.M. said:
With the given interval and the given ratio, you may have two sets of answers that you need to report: one for values in the 1st quad., and one for values in the 2nd quad.
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there is only one, where cos a is negative. I just don't understand why.
 
Loki123 said:
there is only one, where cos a is negative. I just don't understand why.
Click to expand...
Please post the EXACT problem. If it is a part of a bigger problem, post the bigger problem.

Sometimes the answer lies in the "physics" of the problem.
 
Subhotosh Khan said:
Please post the EXACT problem. If it is a part of a bigger problem, post the bigger problem.

Sometimes the answer lies in the "physics" of the problem.
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It is not a part of a bigger problem. This is posted exactly as it is written, I promise.
 
Loki123 said:
there is only one, where cos a is negative. I just don't understand why.
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What are the two angles you get with the given sine? Are they both in the required interval?

Or, without actually finding the angles, can you tell from the sine whether they are in that interval?
 
Dr.Peterson said:
What are the two angles you get with the given sine? Are they both in the required interval?

Or, without actually finding the angles, can you tell from the sine whether they are in that interval?
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so sin a = 5/13 which is about 0,4. One angle I would put between Pi/2 and Pi/4, second angle I would put between Pi and Pi/2...
 
Loki123 said:
so sin a = 5/13 which is about 0,4. One angle I would put between Pi/2 and Pi/4, second angle I would put between Pi and Pi/2...
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Really? Is there an angle between pi/4 and pi/2 with that sine? What is the sine of pi/4?
 
Loki123 said:
I need to determine cos a, tan a and cot a if I know sin a = 5/13 with a being from pi/4 to pi... I know how to determine cos, tan and cot, but I don't know how to determine is cos is positive or negative due to alpha's interval... What do I do?
View attachment 30828
Click to expand...
What helps me to understand signs of trig functions is looking at their actual graphs, not unit circles.
 
Loki123 said:
I need to determine cos a, tan a and cot a if I know sin a = 5/13 with a being from pi/4 to pi... I know how to determine cos, tan and cot, but I don't know how to determine is cos is positive or negative due to alpha's interval... What do I do?
View attachment 30828
Click to expand...
50-39 = 110?
110-104=16? I thought that 120-104 = 16, so 110-104 can't also equal 14.
 
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