Review of 7-5

This week in Advanced Math we took two chapter tests – a multiple choice and free response. In chapter seven we learned how to convert units of measurement, find coterminal angles, use formulas in word problems, find sine and cosine, find reference angles, and also find inverses. We were even introduced to the trig chart. In 7-5 we had to use all the functions. Given one function, we were taught how to find the other five. For example:

EXAMPLE 1: Given tan theta = -5/12 for 0 <> pi. Find the other five trig functions.
A). Draw your coordinate plane. (Draw it in the quadrant according to 0 <> pi, which would be quadrant II).
B). Since tan is equaled to y/x, 5 will be y and 12 will be x.
C). Now that we know we’re looking for r, you would use the Pythagorean Theorem to find it.
But since we know that (5, 12, 13) is a Pythagorean Triple, we don’t have to do that step.
D). Now, we can find the other five trig functions. Just plug the numbers into each function.
*** y=5, x=12, r=13 (But remember, it was in quadrant II so x had to be negative in order for that to work, so 12 will be negative when used).

Sin theta = y/r = 5/13
Cos theta = x/r = -12/13
Cot theta = x/y = -12/5
Sec theta = r/x = -13/12
Csc theta = r/y = 13/5

We know that these functions are easy to remember if you know sin, cosine, and tangent.
Cosecant is the reciprocal of sine, secant is the reciprocal of cosine, and cotangent is the reciprocal of tangent. All you do is plug your numbers into the function!

Also, we were taught how to find reference angles. It is the same as section 7-4. You still follow the same steps and if it is a trig chart angle, plug it in.