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# Trigonometry watch

1. Hello,
I have been facing some challenges in finding the cosine and sine and tangent of any angle greater than 360. First of all, I know that is it is equivalent to the sine or cosine or tangent of its equivalent angle and +/- sine or cosine or tangent of the reference angle, but why is that ? Is there any proof anyone can provide.
Second of all, how can we solve this:
Find the equation equal to this
cos(x-770) the answer is cos(x-50) but why?
thanks
2. I can explain you second point using quadrants look at the image below

as you see the first circles going around is 770 degrees it goes around the quadrant (360+360) and this means that when we start from 0 and Go around the guadrant twice then we get 720 degrees now we want the angle reference to the x axis so we do 770-720 = 50 so this tells that cos 770 = cos 50.
at Times you have to take care with the signs like this example below;

here we r looking at another way to write sin (580) as you can see in the pic that we can write it as sin 40 but that angle falls in the third quadrant where all values of sine is negative so we would write our answer as this;
Sin 580 = -sin 40
hope you understand this. if not let me know so that I can try better and let me know how help full was this
3. (Original post by Ramzi Zeidan)
Hello,
I have been facing some challenges in finding the cosine and sine and tangent of any angle greater than 360. First of all, I know that is it is equivalent to the sine or cosine or tangent of its equivalent angle and +/- sine or cosine or tangent of the reference angle, but why is that ? Is there any proof anyone can provide.
Second of all, how can we solve this:
Find the equation equal to this
cos(x-770) the answer is cos(x-50) but why?
thanks
I don't understand what you are asking in you first question too
4. (Original post by brainmaster)
I can explain you second point using quadrants look at the image below

as you see the first circles going around is 770 degrees it goes around the quadrant (360+360) and this means that when we start from 0 and Go around the guadrant twice then we get 720 degrees now we want the angle reference to the x axis so we do 770-720 = 50 so this tells that cos 770 = cos 50.
at Times you have to take care with the signs like this example below;

here we r looking at another way to write sin (580) as you can see in the pic that we can write it as sin 40 but that angle falls in the third quadrant where all values of sine is negative so we would write our answer as this;
Sin 580 = -sin 40
hope you understand this. if not let me know so that I can try better and let me know how help full was this
It really was thanksss
5. (Original post by brainmaster)
I don't understand what you are asking in you first question too
How was can we prove that the cos/sin/tan of any angle is equal to the cos/sin/tan of the equivalent angle?
6. (Original post by Ramzi Zeidan)
How was can we prove that the cos/sin/tan of any angle is equal to the cos/sin/tan of the equivalent angle?
7. (Original post by Ramzi Zeidan)
Hello,
I have been facing some challenges in finding the cosine and sine and tangent of any angle greater than 360. First of all, I know that is it is equivalent to the sine or cosine or tangent of its equivalent angle and +/- sine or cosine or tangent of the reference angle, but why is that ? Is there any proof anyone can provide.
Second of all, how can we solve this:
Find the equation equal to this
cos(x-770) the answer is cos(x-50) but why?
thanks
http://burymathstutor.co.uk/UnitCircle.html
8. (Original post by Ramzi Zeidan)
Hello,
I have been facing some challenges in finding the cosine and sine and tangent of any angle greater than 360. First of all, I know that is it is equivalent to the sine or cosine or tangent of its equivalent angle and +/- sine or cosine or tangent of the reference angle, but why is that ? Is there any proof anyone can provide.
Second of all, how can we solve this:
Find the equation equal to this
cos(x-770) the answer is cos(x-50) but why?
thanks
tip;
when you are asked such questions and don't know how to solve them or find other angles then then draw quadrants on the side and just see but remember your reference point will always be from the X AXIS!!!! and other questions like sin theta = 1/2, find values for theta in the range 0 to 360 degrees then draw quadrants again and they will tell you what other values of theta satisfy sin theta = 1/2...
9. (Original post by brainmaster)
tip;
when you are asked such questions and don't know how to solve them or find other angles then then draw quadrants on the side and just see but remember your reference point will always be from the X AXIS!!!! and other questions like sin theta = 1/2, find values for theta in the range 0 to 360 degrees then draw quadrants again and they will tell you what other values of theta satisfy sin theta = 1/2...
Thanks
10. your welcome you can ask further questions if you don't understand a part. At start I never understood this but drawing the quadrants and stiff made my understanding better so you can do that too

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