Inverse Trigonometric Functions - Stephanie Perez
(y) Inverse Trig Function
The inverse SINE function is defined by y= arcsin x if and only if sin= x
The domain of y = arcsin x is [ -1, 1]
The range of y = arcsin x [ -𝝅 / 2, 𝝅 / 2]
* Arcsin values only come from Q1 *
(x) Inverse Trig Function
The inverse COSINE function is defined by y = arccos x if and only if cos y= x
(y= arccos x is the an
gle whose cosine is x)
The domain of y= arccos x is [ -1, 1]
The range of y= arccos x is [ 0, 𝝅]
*Cosine can be found in Q1 and Q2
Solving Using a Triangle
It would be very convinient of you to know SOHCAHTOA. That way it would be a lot easier. Not only that drawing a triangle would definitely help out. You will use the same previous steps if you encounter arcsin or arccos but there's also arctan. When arctan appears you should know that that represents (y/x) but there would be more about this is a separate document to get a better understanding of it. HELPFUL HITS
Make sure to use a unit circle! This will make this topic a lot easier! SOH/CAH/TOA
(S)= sine and its set up to look like (O)pposite/ (H)ypotenuse in fraction form
(C)= cosine and it's set up to look like (A)djecent/ (H)ypotenuse in fraction form
(T)= tan and it's set up to look like (O)pposite/ (A)djecent in fraction form
Cos (x) -------------------> Sec (1/x)
Sin (y) --------------------> Csc (1/y)
Tan (y/x) ------------------> Cot (x/y)
Oblique Triangles
Law of Sines
*ONLY for NON RIGHT ANGLE TRIANGLES*
Is it a right triangle? If it is then you will use SOHCAHTOA
If it is not then you will use Law of Sines
Law of Sines: Sin A = Sin B = Sin C
a b c
a = b = c
Sin A Sin B Sin C
The best way to represent this would be by using a Triangle.
* How fat/thin the angle is determines how long the line is*
* You need to know 2 sets*
The Ambiguous Case
This occurs when one uses the law of sines to determine missing measures of a triangle when given two sides and an angle opposite one of those angles (SSA). Height= b x Sin A
How to determine the number of triangles we are going to have
If a=h, then there is only ONE triangle
If a is < h, there is NO triangle
If a > b, there is ONE triangle
If h < a < b, there is TWO triangles
There will be more examples is the “Photos” section
Law of Cosine
It is a different concept then Law of Sines but we of course still use triangle! a²= b² + c² - 2 x c x b x cos A
b²= a² + c² - 2 x a x c x cos B
c²= b² + a² -2 x a x b x cos C
Further explanations and examples are to be posted in the photos and home section. Area of an Oblique Triangle
* Two sides and Angle SSA*
area= ½ bc x Sin A area= ½ ac x Sin B area= ½ ab x Sin C
Make sure to label the triangle ABC and abc based on the side and angles provided on the problem. More examples and into depth explanations on how to do it will be provided in the videos, photos, and home.
