-
Home
- Algebra and trigonometry
- The unit circle: sine and cosine
- The other trigonometric functions
Key equations
Tangent function |
|
Secant function |
|
Cosecant function |
|
Cotangent function |
|
Key concepts
- The tangent of an angle is the ratio of the
y -value to the
x -value of the corresponding point on the unit circle.
- The secant, cotangent, and cosecant are all reciprocals of other functions. The secant is the reciprocal of the cosine function, the cotangent is the reciprocal of the tangent function, and the cosecant is the reciprocal of the sine function.
- The six trigonometric functions can be found from a point on the unit circle. See
[link]
.
- Trigonometric functions can also be found from an angle. See
[link] .
- Trigonometric functions of angles outside the first quadrant can be determined using reference angles. See
[link] .
- A function is said to be even if
and odd if
for all
x in the domain of
f.
- Cosine and secant are even; sine, tangent, cosecant, and cotangent are odd.
- Even and odd properties can be used to evaluate trigonometric functions. See
[link] .
- The Pythagorean Identity makes it possible to find a cosine from a sine or a sine from a cosine.
- Identities can be used to evaluate trigonometric functions. See
[link] and
[link]
.
- Fundamental identities such as the Pythagorean Identity can be manipulated algebraically to produce new identities. See
[link] .The trigonometric functions repeat at regular intervals.
- The period
of a repeating function
is the smallest interval such that
for any value of
- The values of trigonometric functions can be found by mathematical analysis. See
[link] and
[link]
.
- To evaluate trigonometric functions of other angles, we can use a calculator or computer software. See
[link] .
Section exercises
Verbal
On an interval of
can the sine and cosine values of a radian measure ever be equal? If so, where?
Yes, when the reference angle is
and the terminal side of the angle is in quadrants I and III. Thus, a
the sine and cosine values are equal.
Got questions? Get instant answers now!
For any angle in quadrant II, if you knew the sine of the angle, how could you determine the cosine of the angle?
Substitute the sine of the angle in for
in the Pythagorean Theorem
Solve for
and take the negative solution.
Got questions? Get instant answers now!
Tangent and cotangent have a period of
What does this tell us about the output of these functions?
The outputs of tangent and cotangent will repeat every
units.
Got questions? Get instant answers now!
Algebraic
For the following exercises, find the exact value of each expression.
For the following exercises, use reference angles to evaluate the expression.
If
and
is in quadrant III, find
and
Got questions? Get instant answers now!
Questions & Answers
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Omeprazole
Cimetidine / Tagament
For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
how does the stomach protect itself from the damaging effects of HCl
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
function of digestive
Ali
what is the normal body temperature
please why 37 degree selcius normal temperature
Mark
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
how does Lysin attack pathogens
Diya
I information on anatomy position and digestive system and there enzyme
anatomy of the female external genitalia
Organ Systems Of The Human Body (Continued)
Organ Systems Of The Human Body (Continued)
what's lochia albra
Kizito
Got questions? Join the online conversation and get instant answers!
Source:
OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.