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Analyze the Damped Motion
Graph the Sum of Two Functions
Solve for the Area of SSS Traingfles
Solve for the Area of SAS Triangles
Solve Applied Problems
Solve SSS Triangles
Solve SAS Trangles
Solve to Applied Problems
Solve SSA Triangles
Solve SAA or ASA Triangles
The opposite side of the right angle is called the hypotenuse
Express Products as Sums
Express Sums as Products
Use the derive formulas for writing the products of sines or cosines as sums or differences
Double- Angle Formulas to find Exact Values
Find Exact Values
Find Established Identities
In order to find the formulas use:
Use the Unit Circle to find the formulas
The derivation of trigonometric identities by obtaining formulas involves the sum or the difference of two angles
For every value of x both of the functions are defined
Identically Equal, Identity, and Conditional Equations
Two functions f and g are identically equal
f(x)=g(x)
Solving Equations by a Single Trigonometric Function
Using a Graphing Utility
Fundamental Identities
Quadratic in Form
Using a calculator
Define the Inverse Secant, Cosecant, and Cotangent Functions
Most calculators do not have the keys to find the inverse cotangent, cosecant, or secant function
Evaluate them by converting the inverse trigonometric functions
Define the Inverse Sine Function and the horizontal line y=b and where b is between the -1 and 1
Intersects the graph of y=sin x infinitely many times for the horizontal line test
Angle in Standard Position: Vertex is at the origin
1 Degree = 1/ 360 revolution
1 Radian= The measure of a central angle of a circle and the length is equal to the radius of the circle.
Unit Circle= A circle with the radius of 1 unit, and the centered origin of the coordinate plane.
sine (sin)= length of the side opposite the angle to the length of the hypotenuse
cosine (cos)= an angle in a right triangle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse
tangent (tan)= ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
cosecant (csc) = csc(0)=1/sin(0)
secant (sec)= sec(0)-1/cos(0)
cotangent(cot)= cot(0)=1/tan(0)
Angles, Arc Length, and Circular Motion
Distinguish the linear speed v of the object
w= 0/t
v= s/t
0 measured in radians, is a central angle of this circle.
consider a circles of a radius r and two central angles
Theorem Area of a Sector
The area A of the sector of a circle of radius r formed by a central angle of 0 radians
Subdivisions of a degree may be obtained by the use of decimals, the notion of minutes and seconds
One minute , is 1/60 degree
One second, 1/3600 degree
1 counterclockwise revolution= 360 degrees
The angle is formed by the rotating initial side that is exactly once in the counterclockwise and direction to = 1 revolution
One degree, is 1/360 revolution
When a ray, or half-line is a portion of a line that starts at a point V on the line and extends the indefinity in 1 direction
When two rays are drawn into the common vertex they form a ray of angle for the initial side
An angle 0 = standard position for the vertex at the origin of the rectangular coordinate system and the initial side for the coincides and positive x-axis