Monica wrote to me recently:<\/p>\n
\nIn some of my math rules, it says that cos(-t)=cos(t) and sin(-t)=-sin(t)Why is the cos not changed to -cos(t) like the sin function is changed?<\/p>\n<\/blockquote>\n
I replied:<\/p>\n
\nHello Monica<\/p>\n
Grab your calculator and try the following.<\/p>\n
sin 35° (write down the answer)<\/p>\n
sin (-35°) (write down the answer - what can you conclude?)<\/p>\n
Now, try it again, this time:<\/p>\n
sin 88°<\/p>\n
sin (-88°) Did the same thing happen?<\/p>\n
Then try these 2, with cosine:<\/p>\n
cos 50° (write the answer)<\/p>\n
cos (-50°) (what can you conclude this time?)<\/p>\n
To check your conclusion consider this pair:<\/p>\n
cos 20°<\/p>\n
cos (-20°)<\/p>\n
These sort of \"rules\" are given to you in your text book as a summary of what someone discovered in the past. This is a good example where it is better that you discover it yourself - then the rule will make sense and you are more likely to remember it too.<\/p>\n<\/blockquote>\n
Of course, we cannot get students to discover everything they need to know (you would never get through all the content).<\/p>\n
But when math lessons are 100% rules- and formula-based, it is not surprising to get a question like this.<\/p>\n