State all the angles between 0 degrees and 360 degrees that make each equation true.

Hi emilyliv

Here are my answers, download attachment

sin45 = sin ?
cos ? = -cos(-60)
tan 30 = tan ?
tan 135 = -tan ?

Thank you, but for b) I didn't understand how you got the 240. I was also confused about that chart you used for b) and c) do you mind explaining it?

Okay, think of it this way. When you calculate -cos(-60) into your calculator, you get -0.5 (you can verify that yourself if you like)...

Always take the absolute of that number, so for -0.5, the absolute is |-0.5|, where you get 0.5.

Next, take the inverse of cos-1(0.5), you get 60 degrees.

Now, before you took the inverse, 0.5 was actually -0.5. As per the CAST rule, cosine is ONLY NEGATIVE in the 2nd and 3rd quadrant (see diagram below), that means our angles have to be between 90 and 180 AND 180 and 270.



To get the unknown angle in 2nd quadrant, you take 180 minus 60 = 120. To get the unknown angle in the 3rd quadrant, take 180 + 60 = 240.

I teach this method all the time to my students, here's a video of how it's done:





Hope this helps, let me know if you're still having trouble.

Yes, that helps Thanks!