Maths Problems (1 Viewer)

[od9895]

Hello
Could someone please help me with these questions and show all working

Change the following to positive acute angles(there are 2 answers for each)
1. cos(-30)
2. tan(-50)
3. tan(660)

Change the following to their opposite trigonometric ratio with acute angles
1. cot 44
2. tan 216
3. sin 820

Also, could you guys please show me how to label the tan and cot axis on the unit circle

Thanks

 

[deswa1]

Do you know the unit circle (ASTC)? I can't draw it but I'll show you the working for a few of them:
1. cos(-30) is in the fourth quadrant (+) and has a 'base' angle of 30 degrees. cos is positive in the first and fourth quadrants. Therefore cos(-30)=cos30 or cos330.
3. tan(660)=tan(360+300)=tan300. This is in the fourth quadrant and therefore tan is negative. Tan is negative in second and fourth. Therefore tan(660)=tan(300) or tan(120)

1. cotx=1/tanx (definition). Therefore cot44=1/tan44. But both cot and tan are positive in the third quadrant (sine and cos are both negative). Therefore cot44=cot224. cot44=1/tan224.
2. sin820=sin100=sin80. sinx=1/cosecx. Therefore sin820=1/sin100 or 1/sin80.

I hope that makes sense, I explained it badly. Anyway, have a go at the other two and see how you go...