Section 1.5 Identities and Reference angles

Today we discussed Section 1.5 (starting on page 81 in the text book). This section is all about identities, and reference angles, but we focused on identities today.

An identity is an equation that is satisfied for all values of the variable for which both sides are defined. Some examples are: x+x=2x, and x/x=1.

The Fundamental identity for any and all real numbers is: Sin² α+cos²α=1 but we can rearrange this identity into two other equations to make life a little bit easier.

cosα=±√(1-sin²α)

sinα=±√(1-cos²α)

If you're trying to find cosine and you are given the value of sine, try plugging it into the first equation or vice versa. The important thing to keep in mind here is that you will be told the quadrant in which the angle lies. This is important when you are deciding whether the value of sine or cosine is positive versus negative. Here's a handy little chart on that!

When you don't have this handy dandy chart, think about it logically: r is the distance from (x,y) to the origin, so r has to be positive (distances can't be negative). Then if x or y is negative. Sine, cosine, secant, and cosecant will also be negative, because a positive multiplied or divided by a negative is a negative.

I hope this has all made sense! Please let me know if you have questions!

See you tomorrow,

Elizabeth