Expert I Trigonometry (11) Flashcards
What are the main angles that you should be able to find in standard position?
You can use math from there but it is handy to have these four memorized as well as noticing that there are 360 degrees in a circle.
This way you should be able to draw the angle in standard position in order to find the reference angle (the angle as measured to the x-axis under or including 90 degrees).
What quadrants are automatically used for the primary trigonometric ratios?
If you are trying to find the angle from the ratio, you will notice that a negative ratio could mean the angle is in one of two quadrants since it is impossible for your calculator to know which of the side lengths was negative and which was positive.
The calculator will always return an angle in quadrant 1 if it exists. If that does not exist it will then try to return the angle in quadrant 4. If that does not exist either, then it will give you an angle in quadrant 2.
I just remember 1,4,2 and that helps.
So when working with degrees between 0 and 360, you may need to draw a picture and know where the ratios are positive and negative.
See the picture for a summary of where they are positive.
What trigonometry can we use if we do not have a right triangle?
sine law and cosine law are for use with any triangle
What is the sine law?
Sine law is a way of finding a missing angle or side given three other pieces of information (either two sides or two angles, and then one of the other).
Remember to watch out for the ambiguous case.
What is the cosine law?
Cosine law is a way of finding a missing angle or side in a triangle when you have three pieces of information and need to find the fourth, where one of those is an angle and the other three are side lengths.
Remember to watch out for the ambiguous case.
What is the ambiguous case?
The Ambiguous Case of the Law of Sines states that when using the law of sines to find a missing side length, the possibility of two solutions for the measure of the same side may occur. This ambiguous case occurs most often when two sides and a non-included angle of a triangle are given.
In the ambiguous case, SSA, the Law of Sines is easier to apply, but there will be two possible angles, and we must check each angle to see if it produces a solution. Using the Law of Cosines involves solving a quadratic equation, but each positive solution of the equation yields a solution of the triangle.
Describe the ambiguous case SSA where you are using the sine law and no triangle exists.
Describe the ambiguous case SSA where you are using sine law and two different triangles exist
Describe a situation where you have SSA and the sine law and only one triangle exists.
Summarize the ambiguous case SSA with law of sines.
