Finding the values (or ratios) of

sine and

cosine for the

unit circle is very easy given that you can

memorize a simple table of values. The table for cosine goes like this:

cos0 = sqrt4/2 = 1

cos30 = sqrt3/2

cos45 = sqrt2/2

cos60 = sqrt1/2 = 1/2

cos90 = sqrt0/2 = 0

If you notice, is starts with sqrt4/2 and with each of these

angles the value of the number having the

square root decreases by one in each step until it reaches 0.

Likewise, here is the table for sine. Sine's table is the

inverse of cosine's, so it should be easy to

remember.

sin0 = sqrt0/2 = 0

sin30 = sqrt1/2 = 1/2

sin45 = sqrt2/2

sin60 = sqrt3/2

sin90 = sqrt4/2 = 1

Because we know that

tangent is sine/cosine, we can find the value of tangent by putting the

exact value of sine or that of cosine. The 2s of the

denominator will always cancel out so you can just put the

numerator of sine over cosine's. In the same way, we know that

secant and

cosecant are the

inverse of cosine and sine so we can find these values also. Simply take the

reciprocal of the sine, cosine, or even tangent (for

cotangent) to find their inversed values. If the denominator need rationalizing, do so by multiplying by a form of 1.