Math (Trigonometry) Help

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My teacher gave us a sheet for HW and one of the parts is: Solve the following questions without a calculator: 1. cos (7π) 2. sin(62)csc(62) 3. sin(80)sin(10)
And we have to show work to show that we sidnt use a calculator. How do you solve these problems?
Thanks alot for your help!

1. this should be under the school board

2. google is your friend, don't google the answers but how to sine, cosine and tangent by hand.

soh cah toa... (sin: opposite/hypotenuese, cosine: adjacent/hypotenuese, tan: opposite over adjacent)

Draw a triangle on the unit circle to make this easier.

Sine is the verticle arm of a triangle on the unit circle, Cosine is the horizontal arm.

cos(7*pi) is the same as cos(pi), and for the other two, use trig identities to make it easier. As for sin62*csc62 there should be an identity that shows that sin(x)*csc(x)=1 for all x, x != 0 + n*pi where n is an integer.

as for csc(x), that is 1/sin(x).

Here's the wiki link http://en.wikipedia.org/wiki/Trigonometric_functions
It kinda explains what it is you are doing.

Either way, my best advice is to read through your textbook. Maybe consider supplementing your textbook with a "For Dummies" version. I did that a lot in college.

Oh, and now I'm reading Padium's advice... I like that soh cah toa. Yeah, the wiki article explains the reciprocals (csc which is the reciprocal of sin) like the reciprical of 3/4 is 4/3. Sorry that I forget how to work with trig beyond the simple basics.

And for number 2, being the dummy I am I need to simplify, wouldn't multiplying anything by its reciprocal equal 1? Like 1/2 times 2/1 equals 2/2 which equals 1. 3/4 times 4/3 equals 12/12 which is 1. Unless you are dealing with zero because it doesn't have a reciprocal (1/0 would be a no solution), or would you work with it like it would and then the answer be zero?

Outside of that, I think it's more like algebra with trig symbols as opposed to just x. I personally totally forget how to do that without the aid of a textbook review.

You could ask your teacher if it is OK to use a set of sine cosine and tangent tables, these are slightly less accurate than a modern calculator but they are a good and useful way to get the sine, cosine or tan values for a given angle.

I am not sure how many teachers now tell their kids about mathmatical tables, I used them a little in my youth.

There are only a few angles you need to know: 30, 45, 60, 90... All math a teacher gives you that they ask not to use a calculator will always break down into 1) those angles. 2) for other things, like the reciprocal, will break down into rational numbers. They will never ask you to compute sin(83 degrees) or the square root of two. They give you a question, they want you to use rationals, or symbols representing a specific irrational number.