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Home
- Algebra and trigonometry
- The unit circle: sine and cosine
- Unit circle
Key equations
Cosine |
|
Sine |
|
Pythagorean Identity |
|
Key concepts
- Finding the function values for the sine and cosine begins with drawing a unit circle, which is centered at the origin and has a radius of 1 unit.
- Using the unit circle, the sine of an angle
equals the
y -value of the endpoint on the unit circle of an arc of length
whereas the cosine of an angle
equals the
x -value of the endpoint. See
[link] .
- The sine and cosine values are most directly determined when the corresponding point on the unit circle falls on an axis. See
[link] .
- When the sine or cosine is known, we can use the Pythagorean Identity to find the other. The Pythagorean Identity is also useful for determining the sines and cosines of special angles. See
[link] .
- Calculators and graphing software are helpful for finding sines and cosines if the proper procedure for entering information is known. See
[link] .
- The domain of the sine and cosine functions is all real numbers.
- The range of both the sine and cosine functions is
- The sine and cosine of an angle have the same absolute value as the sine and cosine of its reference angle.
- The signs of the sine and cosine are determined from the
x - and
y -values in the quadrant of the original angle.
- An angle’s reference angle is the size angle,
formed by the terminal side of the angle
and the horizontal axis. See
[link] .
- Reference angles can be used to find the sine and cosine of the original angle. See
[link] .
- Reference angles can also be used to find the coordinates of a point on a circle. See
[link] .
Section exercises
Verbal
Discuss the difference between a coterminal angle and a reference angle.
Coterminal angles are angles that share the same terminal side. A reference angle is the size of the smallest acute angle,
formed by the terminal side of the angle
and the horizontal axis.
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Algebraic
For the following exercises, use the given sign of the sine and cosine functions to find the quadrant in which the terminal point determined by
lies.
For the following exercises, find the exact value of each trigonometric function.
Questions & Answers
find the equation of the tangent to the curve y=2x³-x²+3x+1 at the points x=1 and x=3
derivative of logarithms function
how to solve this question
sidra
ex 2.1 question no 11
khansa
anyone can help me
khansa
ex 2.1 question no. 11
khansa
Find the derivative of g(x)=−3.
any genius online ? I need help!!
need to learn polynomial
Zakariya
plz help me in question
Abish
evaluate the following computation (x³-8/x-2)
teach me how to solve the first law of calculus.
teach me also how to solve the first law of calculus
Bilson
only god knows😂
abdulkadir
f(x) = x-2
g(x) = 3x + 5
fog(x)?
f(x)/g(x)
fog(x)= f(g(x))
= x-2
= 3x+5-2
= 3x+3
f(x)/g(x)= x-2/3x+5
diron
pweding paturo nsa calculus?
jimmy
how to use fundamental theorem to solve exponential
find the bounded area of the parabola y^2=4x and y=16x
what is absolute value means?
(mathematics) For a complex number a+bi, the principal square root of the sum of the squares of its real and imaginary parts, √a2+b2 . Denoted by | |.
The absolute value |x| of a real number x is √x2 , which is equal to x if x is non-negative, and −x if x is negative.
Ismael
find integration of loge x
find the volume of a solid about the y-axis, x=0, x=1, y=0, y=7+x^3
Can calculus give the answers as same as other methods give in basic classes while solving the numericals?
y=(x^2 + 3x).(eipix)
Claudia
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Source:
OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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