Reflection 1

In this reflection I am going to talk about how to find relationships among trig functions. To simplify these you would first you would check identities. cscX = 1/sinX, secX = 1/cosX, cotX = 1/tanX, tanX = sinX/cosX, cotX = cosX/sinX. Other identities are sin^2X + cos^2X = 1, 1 + tan^2X = sec^2X, 1 + cot^2X = csc^2X. There are also identities for negative relationships: sin(-X) = -sinX and cos(-X) = cosX, csc(-X) = -cscX and sec(-X) = secX, tan(-X) = -tanX and cot(-X) = -cotX. And now for the identities of the cofunction realationships: sinX = cos( 90 degrees-X) and cosX = sin(90 degrees-X), tanX = cot(90 degrees-X) and cotX = tan(90 degrees-X), secX = csc(90 degrees-X) and cscX = sec(90 degrees-X). Second you would see if you could use simple algebra, as in factoring or completing the square. Then u would check your identities and keep this process up until u come up with a simple answer.

So in the example: secX - sinXtanX

You would switch out the secX with 1/cosX and switch the tanX with sinX/cosX. Now it would look like 1/cosX - sinx(sinX/cosX)

Then you would distribute the sinX and get 1 - sin^2X/cosX

Then you would look at the sin^2X + cos^2X = 1. Now you would have to try to get 1 - sin^2X on one side so you would subtract the sin^2X. Then you would replace 1 - sin^2X in the equation with cos^2X to get cos^2X/cosX

Now you would use simple algebra and divide to get the answer of cosX