The angles, 60°, [tex]\displaystyle \frac{\pi}{4}[/tex] and [tex]\displaystyle \frac{\pi}{6}[/tex] are special angles that have known trigonometric ratio values.
First part;
The sine and cosine gives the coordinates of the tip of the radius of a unit circle as it rotates P(cos(θ), sin(θ))Second part;
With the knowledge of the sine and cosine of 60°, we have; sin(60°) = sin(120°), sin(240°) = -sin(60°), sin(300°) = -sin(60°)cos(120°) = -cos(60°), cos(240°) = -cos(60°), cos(300°) = cos(60°)Third part;
[tex]\displaystyle \frac{\pi}{4}[/tex] can be used to find the sine and cosine of [tex]\displaystyle \frac{3 \cdot \pi}{4}[/tex], [tex]\displaystyle \frac{5 \cdot \pi}{4}[/tex], and [tex]\displaystyle \frac{7 \cdot \pi}{4}[/tex] [tex]\displaystyle \frac{\pi}{6}[/tex], can be used to find the sine and cosine of [tex]\displaystyle \frac{5 \cdot \pi}{6}[/tex], [tex]\displaystyle \frac{7 \cdot \pi}{6}[/tex], and [tex]\displaystyle \frac{11 \cdot \pi}{6}[/tex]Reasons:
First Part;
Considering a unit circle with the center at the origin of the graph, we have;
The sine of the angle, θ, rotated by the radius is the vertical distance of a point P on the circle which is the location of the radius, from the horizontal axis.
The cosine of the angle, θ, is the horizontal distance of P from the vertical axis, such that we have;
The coordinates of point P = (cos(θ), sin(θ))
In the four quadrant, we have;
First Quadrant; All trigonometric ratios are positive
Second Quadrant; sine is positive
Third Quadrant; Tan is positive
Fourth Quadrant; Cosine is positive
Second part;
We have; At 120°, the point P is the same elevation from the horizontal axis, therefore;
sin(60°) = sin(120°) = 0.5·√3
However, the x-coordinate of the point P is in the negative direction, therefore, we get;
cos(120°) = -cos(60°) = -0.5
Similarly from the quadrant relationship, we have;
240° is in the third quadrant, and it is 60° below the negative horizontal line, therefore;
sin(240°) = -sin(60°) = -0.5·√3
cos(240°) = -cos(60°) = -0.5
300° is in the fourth quadrant, and it is 60° below the positive x-axis, therefore;
sin(300°) is negative and cos(300°) is positive
Which gives;
sin(300°) = -sin(60°) = -0.5·√3
cos(300°) = cos(60°) = 0.5
Third part;
[tex]\displaystyle \frac{\pi}{4} =45^{\circ}[/tex]
[tex]\displaystyle \frac{\pi}{6} =30^{\circ}[/tex]
The sine and cosine of 45° can be used to find the sine and cosine of (180° + 45°) = 225°, (360° - 45°) = 315°
Also, due to the mid location of the angle 45° on the quadrant, we have;
Another angles is the sines and cosine of (90° + 45°) = 135°
Therefore, [tex]\displaystyle \frac{\pi}{4}[/tex], can be used to find the sine and cosine of 135°, 225°, and 315°
[tex]\displaystyle 135^{\circ} = \mathbf{\frac{3 \cdot \pi}{4}}[/tex], [tex]\displaystyle 225^{\circ} = \frac{5 \cdot \pi}{4}[/tex], [tex]\displaystyle 315^{\circ} = \frac{7 \cdot \pi}{4}[/tex]
Therefore,
[tex]\displaystyle \frac{\pi}{4}[/tex] can be used to find the sine and cosine of [tex]\displaystyle \mathbf{\frac{3 \cdot \pi}{4}}[/tex], [tex]\displaystyle \mathbf{\frac{5 \cdot \pi}{4}}[/tex], and [tex]\displaystyle \mathbf{ \frac{7 \cdot \pi}{4}}[/tex]
Similarly, the sine and cosine of, [tex]\displaystyle \frac{\pi}{6}[/tex] = 30° can be used to find the sine and cosine of 150°, 210°, and 330°.
[tex]\displaystyle 150^{\circ} = \frac{5 \cdot \pi}{6}[/tex], [tex]\displaystyle 210^{\circ} = \frac{7 \cdot \pi}{6}[/tex], and [tex]\displaystyle 330^{\circ} = \frac{11 \cdot \pi}{6}[/tex]
[tex]\displaystyle \frac{\pi}{6}[/tex], can be used to find the sine and cosine of [tex]\displaystyle \mathbf{ \frac{5 \cdot \pi}{6}}[/tex], [tex]\displaystyle \mathbf{ \frac{7 \cdot \pi}{6}}[/tex], and [tex]\displaystyle \mathbf{\frac{11 \cdot \pi}{6}}[/tex]
Learn more about the sine and cosine of angles here:
https://brainly.com/question/4372174
Answer:
Step-by-step explanation:
The cosine value of an angle is the x coordinate of the point the angle corresponds to on the unit circle, and the sine value of an angle is the y coordinate of that point. 120, 240, and 300 all form 60 degree reference angles which in turn forms 30-60-90 triangles which help to find the sine and cosine of these corresponding angles. Pi/4 radians converts to 45 degrees which forms a 45-45-90 special triangle on the unit circle which has its own known trigonometric ratio. Pi/6 radians converts to 30 degrees which forms a 30-60-90 triangle on the unit circle which also has a known trigonometric ratio. These ratios help find the sine and cosine of the angles on the unit circle which corresponds to a point on the coordinate plane.
The thickness of a grain of pepper is 2.3 x 10-2 inches. How many inches are 100 grains of pepper? Express your answer in scientific notation.
Answer:
230.0 x 1000-200
Step-by-step explanation:
Since one grain of pepper is 2.3x10-2 100 would be 100 times that.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
72
The measure of angle is 4. The measure of its reference angle is
and tan eis
Step-by-step explanation:
the reference angle is the smallest angle difference between the defining terminal arm of the angle and the x-axis. it is always positive.
if an angle is smaller than 90°, then it is is own reference angle.
7pi/4 is 1pi/4 (or simply pi/4) short of a full circle (2pi or 8pi/4).
therefore, if is easy to see that this pi/4 is the reference angle (45°).
tan(7pi/4) = -1, while tan(pi/4) = 1.
for every 45° angel in every quadrant the absolute values of sine and cosine are equal.
but in quadrant 1 both, sine and cosine, are positive, while in quadrant 4 sine is negative and cosine is positive.
and since tan = sine/cosine, this gives us the results above.
A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 19 feet more than the length of the shortest side. Find the dimensions if the perimeter is 167 feet.
PLS PLS HELP
Evaluate 5−1/−90. Write your answer as a fraction in simplest form.
Answer:
2/-45
Step-by-step explanation:
5-1 = 4
4/-90 = 2/-45
Hope that helps
what are integer solutions to the equality below-2 < x < 2
Answer:
-1, 0, 1
Step-by-step explanation:
Intengers are whole numbers. those 3 numbers are the only intengers between -2 and 2
/ why we use this symbol
The slash is an oblique slanting line punctuation mark /. Once used to mark periods and commas, the slash is now most often used to represent exclusive or inclusive or, division and fractions, and as a date separator.
To become a member of the book-of-the-month club there is a $40 sign-up fee and a $2 monthly fee. Write an equation in slope-intercept form that models this situation.
Answer:
y = 2x + 40
Step-by-step explanation:
slope-intercept formula: y = mx + b
x = number of months
y = total cost
slope is 2 and y-intercept is 40
Trevor earns $7.80 an hour take home pay and works 20 hours each week. Trevor wants to buy a new laptop computer to take to college that costs $780. How many weeks will it take for Trevor to achieve his goal? a. 4 weeks b. 5 weeks c. 6 weeks d. 7 weeks
Answer:
5 weeks
Step by step
7.80 x 20 = 156
156 x 5 = 780
Answer: B) 5 weeks
Step-by-step explanation: I know your struggling and that's why you need this answer. your welcome cutie.
Arthur paid $0.84 for 0.25 pound of potato salad. How much does one pound cost?
Answer:
$3.36 per pound
Step-by-step explanation:
The information gives us that 1/4 a pound of salad costs $0.84, to get to one pound all we have to do is multiply $0.84 by 4 to get our pound price.
0.84*4= $3.36
Brainliest would be appreciated! :-)
Aaron travels a distance of 680 miles in 8 hours by train. What is the speed of the train?
A.
75 miles/hour
B.
80 miles/hour
C.
85 miles/hour
D.
90 miles/hour
Answer:
C 85 miles/hour
Step-by-step explanation:
680 / 8 = 85
132 divided by 0.11 i need help ;-;
Answer:
Step-by-step explanation:
1. 132+0.11
2. Answer is 1200
Entering it in Your Calculator
(132 Divided by 0.11)
= 1200
heeeeeelllllppppppp please
Answer: D. <Q ≅ <T
Step-by-step explanation:
This satisfies the ASA Congruency Theorem.
At a restaurant your total bill is $45. Sales tax is 5%. What is your total bill after tax?
Answer:
47.25
Step-by-step explanation:
Heres how I found the answer:
if sales tax is 5%, then we need to find 5% of 45 and add it to 45!
5% of 45= 2.25
(I found this by doing 45*5%, or 45*.05)
Now, add 2.25 to 45!
Total bill=47.25 dollars
Hope I could help!
what is .072 divided by 345.00
Answer:
Step-by-step explanation: if its .072
or if it 0.72/345.00
0.00208695652
Erin and Jamie are collecting shells while the tide is out Erin has 27 shells and she has 9 more shells than Jamie write an equation for this situation and find how many shells Jamie has collected
Answer:
27-9= 18
Step-by-step explanation:
Erin's total shells is 27, her total is 9 more shells than Jamie has. Thus you subtract 9 from 27 to get the number of shells Jamie collected.
Solve.
(Sorry About my handwriting)
Answer: the answer is gonna be a decimal which is Decimal: 145.333333 the 3 is repeated it keeps going forever
Percentage of words starting with T
WHAT IS 10x+55 = 100
Answer:
[tex]x=\cfrac{9}{2}\: or\: x=4.5[/tex]
Step-by-step explanation:
[tex]10x+55 = 100[/tex]
[tex]10x+55-55=100-55[/tex]
[tex]10x=45[/tex]
[tex]\cfrac{10x}{10}=\cfrac{45}{10}[/tex]
[tex]x=\cfrac{9}{2}[/tex]
HOPE IT HELPS!
Subtract 55 from both sides.
10x=100-55
Simplify 100-55 to 45.10x=45
Divide both sides by 10.
[tex]x = \frac{45}{10} [/tex]
Simplify[tex]x = \frac{9}{2} [/tex]
In the figure shown below find the value of a, round to the nearest tenth.
What Pic or Figure Lol
Construct a 60angle
NEEDED ASAP LIKE IN 5 MINUTES OR LESS
Answer:
but how there is nothing i dk plz can you explain me what the question actually is?
Use the function z=7c to find the value of z when c=8.
Answer:
z = 56
Step-by-step explanation:
z = 7(8)
An ant looks up at an angle of elevation of 30degrees to the top of a tree. If the ant is 40 feet from the base of the tree, what is the height of the tree, to the nearest tenth?
a.
23.1 feet
b.
25.2 feet
c.
32.8 feet
d.
34.6 feet
Anaswer Let the height of the tree be
y
ft. By condition;
tan
38
=
y
43
or
y
=
43
tan
38
or
y
=
33.6
ft [Ans]
Step-by-step explanation:
Answer:
Step-by-step explanation:
The CORRECT answer is
C. 32.8 feet Got it correct
Sally's Stuffed Animal Company charges $0.75 per pound to ship stuffed animals. Part A: Write an equation to determine the total cost, c, to ship p pounds of stuffed animals. Use your equation to determine the cost of shipping 2 pounds of stuffed animals. (6 points) Part B: If the company reduces the cost to ship the stuffed animals by $0.05 per pound, write an equation to determine the total cost, c, to ship p pounds of stuffed animals with the reduced cost. (4 points)
Answer:
i think the person on top of me is correct :)
Step-by-step explanation:
Help please !!!!!!!!
Answer:
yes
Step-by-step explanation:
yes, they are congruent for the AAS rule ( angle angle side)
help please and NO LINKS
Answer:
B
Step-by-step explanation:
A trapezoid has only two parallel sides while a parallelogram has 2 pairs of parallel sides.
PLS HELP MEE
Are the figures similar? If they are what is the scale factor. If they are not please explain why.
Maria's monthly income is $1,250. She can afford to spend 25% of her income for rent. How much can she pay for rent each month?
Answer:
312.5
Step-by-step explanation: 25 percent of 1250 is 312.5(calculated)
to check your answer we multiply 312.5 by 4 as its (25%=1/4)
-3х +2y = -27
3х + 5y = 6
Answer:
Hi it can't be solved because a equation can't have 2 variables
Pls pls I just need the equation to this thank you so much!
Answer:
5.00+5.5+5.10+5.15+5.20+5.25= x
x is whatever the cost is.
if you want x, it is.... 31.2
or
y=5.00+5.5+5.10+5.15+5.20+5.25
If you want the equation in linear form (as in y= _x+b), then it is:
y=0.001x
sorry if im wrong! :D
Step-by-step explanation:
Just ask!
Hope this helps... :)
is it Substitution or linear combination?
Answer:
Substitution
Step-by-step explanation:
You would solve this system using the substitution method as one of the variables are define.
In other words y = x + 3 defines y with the expression "x + 3" and we are easily able to substitute this into the other equation for y and solve of x.