



Key equations
Cosine 
$\mathrm{cos}\text{\hspace{0.17em}}t=x$ 
Sine 
$\mathrm{sin}\text{\hspace{0.17em}}t=y$ 
Pythagorean Identity 
${\mathrm{cos}}^{2}t+{\mathrm{sin}}^{2}t=1$ 
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
$\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ equals the
y value of the endpoint on the unit circle of an arc of length
$\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ whereas the cosine of an angle
$\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ 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
$\text{\hspace{0.17em}}[\mathrm{1},1].$
 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,
$\text{\hspace{0.17em}}t,$ formed by the terminal side of the angle
$\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ 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,
$\text{\hspace{0.17em}}t,$ formed by the terminal side of the angle
$\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ 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
$\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ lies.
For the following exercises, find the exact value of each trigonometric function.
Questions & Answers
By the definition, is such that 0!=1.why?
(1+cosA+IsinA)(1+cosB+isinB)/(cos@+isin@)(cos$+isin$)
how we can draw three triangles of distinctly different shapes. All the angles will be cutt off each triangle and placed side by side with vertices touching
bsc F. y algebra and trigonometry pepper 2
given that x= 3/5 find sin 3x
remove any signs and collect terms of 2(8a3bc)
is that a real answer
Joeval
x²2x+94x²+12x20
3x²+10x+11
Miranda
x²2x+94x²+12x20
3x²+10x+11
Miranda
(X22X+8)4(X23X+5)=0 ?
master
The anwser is imaginary
number if you want to know The anwser of the expression
you must arrange The expression and use quadratic formula To find the
answer
master
The anwser is imaginary
number if you want to know The anwser of the expression
you must arrange The expression and use quadratic formula To find the
answer
master
X22X+84X2+12X20=0
(X24X2)+(2X+12X)+(20+8)= 0
3X2+10X12=0
3X210X+12=0
Use quadratic formula To find the answer
answer (5±Root11i)/3
master
Soo sorry (5±Root11* i)/3
master
x22x+84x2+12x20
x24x22x+12x+820
3x2+10x12
now you can find the answer using quadratic
Mukhtar
explain and give four example of hyperbolic function
What is the correct rational algebraic expression of the given "a fraction whose denominator is 10 more than the numerator y?
Find nth derivative of eax sin (bx + c).
Find area common to the parabola y2 = 4ax and
x2 = 4ay.
Anurag
y2=4ax= y=4ax/2. y=2ax
akash
A rectangular garden is 25ft wide. if its area is 1125ft, what is the length of the garden
to find the length I divide the area by the wide wich means 1125ft/25ft=45
Miranda
What do you call a relation where each element in the domain is related to only one value in the range by some rules?
given 4cot thither +3=0and 0°<thither <180°
use a sketch to determine the value of the following
a)cos thither
nothing up todat yet
Miranda
aap konsi country se ho
jai
which language is that
Miranda
what is the formula for calculating algebraic
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
Miranda
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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