Section 4.7
Law of Sines:
The law of sines can be used to solve triangles.
The ambiguous case:
The ambiguous case:
There are many different possibilities for ambiguous case triangles and you can use the law of sines and law of cosines to solve them. In most cases you will be using the law of sines.
Law of Cosines
Law of Cosines
The law of cosines can be used to find missing angles or missing side measures. All you have to do is plug in the values for the equation.
Heron's Formula
Heron's Formula
This formula is used whenever you are given all the sides of a triangle and want to find the area. the s in the formula stands for all of the sides added together then divided by 2.
Area of a triangle given SAS
This formula is used whenever you want to find the area of a triangle given two sides and an angle. the a and b stand for the sides and then the sin C stands for the angle measure. the letters are interchangeable.
Section 5.1
Reciprocal and Quotient Identities
Here, what you do is you are given an equation and not all of the terms are going to match so you need to try to get each one as similar as possible then you complete the problem and get it in its simplest form.
Pythagorean Identities:
Pythagorean Identities:
When simplifying the equations you may come across Pythagorean identities which can be rearranged to fit what you are looking for in you problem until you have what you need then you can substitute.
Cofunction Identities:
Cofunction Identities:
When you are asked to simplify an equation and it has a cofunction identity in it you can substitute its equivalent into the equation and the continue to solve.
Odd-Even Identities
When simplifying problems you can use the odd-even identities to make the problem positive or negative to help you complete the problem.
section 5.2
Verifying trigonometric identities
Verifying trigonometric functions is easy because you are already given the answer, all you have to do is look at the more challenging side of the equation and then simplify it as you normally would and then keep simplifying it until both sides match. your work is the answer for the equations.
section 5.3
Solving trigonometric equations
When solving trigonometric equations you solve it as if it is a normal equation. Your goal is to isolate the trig function. Once you isolate the trig function and the other side of the equation is in its simplest form you look for the value for whatever trig func you are looking for on the unit circle. if you know the unit circle sin and cos are given to you. You then have to solve for any other trig values using x, y, and r.