How can I solve this trig identity manipulating tan instead of the right side?
Answers
Answer:
Trig identities
[tex]\tan(\theta)=\dfrac{\sin(\theta)}{\cos(\theta)}[/tex]
[tex]\sin(\thet2\theta)=2 \sin(\theta)\cos(\theta)[/tex]
[tex]\begin{aligned}\cos(\thet2\theta) & =1-2\sin^2(\theta)\\2\sin^2(\theta) & = 1-\cos(2\theta) \end{aligned}[/tex]
Solution
[tex]\tan(\theta)=\dfrac{\sin(\theta)}{\cos(\theta)}[/tex]
[tex]\textsf{Multiply by}\:\dfrac{2\sin(\theta)}{2\sin(\theta)}:[/tex]
[tex]\begin{aligned}\implies \tan(\theta) & =\dfrac{\sin(\theta)}{\cos(\theta)} \times \dfrac{2\sin(\theta)}{2\sin(\theta)}\\\\ & =\dfrac{2\sin^2(\theta)}{2\sin(\theta)\cos(\theta)}\\\\ & = \dfrac{1-\cos(2\theta)}{\sin(2\theta)}\end{aligned}[/tex]
Therefore,
[tex]\implies \dfrac{1-\cos(2\theta)}{\sin(2\theta)}=\dfrac{1-\cos(2\theta)}{\sin(2\theta)}[/tex]
Related Questions
A 12 foot ladder is resting against a wall. The base of the ladder is 2.8 feet from the base of the wall.How high up the wall will the ladder reach? Show all work and round to the nearest tenth.
Answers
Answer:
≈11.7 [ft].
Step-by-step explanation:
1) the ladder and the wall form the right triangle, where the length of the ladder (12 ft) is hypotenuse and the distance between the base of the latter and the base of the wall is the shortest side.
2) the longest side can be calculated according the Pythagoras theorem:
[tex]L=\sqrt{12^2-2.8^2}=\sqrt{136.16}=11.7[ft].[/tex]
3x + 14 / 8 = -5
And also need to do the check ♀️
Answers
Hope this helps
The radius of a circle is 3 yards. What is the circle's circumference?
r=3 yd
Use 3.14 for .
yards
Answers
Answer: 18.84
Step-by-step explanation: Circumference is calculated as 2 × 3.14 × radius
Prove that ABCD is not a parallelogram.
Answers
Answer:
Segment AD is 4 units long, while segment BC is 5 units long. If this figure was a parallelogram, these two segments would be equal to each other.
Step-by-step explanation:
2.
Find m∠F.
a.30°
b.60°
c.15°
d.10°
Answers
Answer:
Step-by-step explanation:
[tex]\sf Sin \ F = \dfrac{Opposite \ of \ angle \ F}{hypotenuse}[/tex]
[tex]= \dfrac{9}{18}\\\\= 0.5[/tex]
[tex]F = Sin^{-1} \ (0.5)\\[/tex]
= 30°
distributive property
Answers
Answer:
9 x 6= 9 x ( 3+3 )
= 9 x 3 + 9 x 3
= 27 + 27
= 54
Step-by-step explanation:
Pls help me i am st patrick
Answers
Answer:
7
Step-by-step explanation:
15+2=17
20-17=3
So, these three people definitely like lemonade
11-3=8
So, eight people like both coffee and lemonade
15-8=7
Ans: 7 people like coffee but not lemonade
Taffy Twists candy company keeps the same ratio of pieces of strawberry candy to banana candy in their packs. The Mega Pack has 40 strawberry candies and 50 banana candies. The Party Pack has 20 strawberry candies.
How many banana candies are in the Party Pack?
Answers
Answer:
25 bananas
Step-by-step explanation:
You halved the strawberry number (from 40 to 20) ....half the banana number = 25
Question is in image below.
Answers
Answer:
-9/25, -0.bar 3, √24, 4.92
Answer:
[tex]-\frac{9}{25} < -0.3 < \sqrt{24} < 4.92[/tex]
Step-by-step explanation:
We first have to expand -0.3, -9/25, and sqrt(24). Then we determine which is least and which is greater.
-0.3 = -0.3333...
-9/25 = -0.36
[tex]\sqrt{24}[/tex] ≈ 4.8989799486
4.92
[tex]-\frac{9}{25} < -0.3 < \sqrt{24} < 4.92[/tex]
Paul works at at the bucket of Cracker Barrel and makes $8.25 an hour plus tips. Paul averages $110 in tips during an 8 hour shift. Paul typically works 40 hours A week and he works 48 weeks out of the year the other 2 weeks he gets paid vacation time during this time he earns his base hourly rate for 40 hours a week what is his gross annual income?
Answers
Answer:
330.00
Step-by-step explanation:
i think thats the answer someone would have to double check but this is what i did the get that
How much overtime pay do you get for working 40 hours if you get the following pay scale:
8.25 for all hours up to 40
110 for all hours in excess of 40
Calculate Total Pay
Total Wages = Regular Rate x 40 Hours + Overtime Rate x (Hours - 40)
Total Wages = 8.25 x 40 Hours + 110 x (40 - 40) Hours
Total Wages = 8.25 x 40 Hours + 110 x (0) Hours
Total Wages = 330 + 0
Total Wages = 330.00
A quadrilateral is circumscribed about a circle. The sum of the lengths of its two opposite sides is 21 cm, and the radius of the circle is 5 cm. Find the area of the quadrilateral.
I will give 100 points
Answers
Answer:
105 cm²
Step-by-step explanation:
Properties of a quadrilateral circumscribed about a circle
Each side of the quadrilateral is a tangent to the circle.The sums of the measures of the opposite sides of the quadrilateral are equal. The area of the quadrilateral is half the product of its perimeter and the radius of the circle.Given:
Radius = 5 cmSum of the lengths of its two opposite sides = 21 cmTherefore, the sum of the other pair of opposites is also 21 cm.
So the perimeter = 21 + 21 = 42 cm
[tex]\implies \sf Area=\dfrac12\cdot42\cdot5=105\:cm^2[/tex]
Looking like trapezoid
area:-
1/2(sum of parallel sides)(Height)1/2(21+21)(5)1/2(42)(5)21(5)105cm²CAN SOMEBODY EXPLAIN HOW TO DO THIS IT'S MY 5TH TIME ASKING AND NOBODY EVEN HELPS ME!
i used caps to get ur attention 7u7
Answers
Answer:
10x20+10x6=260
Step-by-step explanation:
Answer:
260 cm²
Step-by-step explanation:
Area of the rectangle
= l × w
= 20 × 10
= 200 cm²
Area of the triangle
= ½bh
= ½ × 20 × 6
= ½ × 120
= 60 cm²
Area of the total figure
= Area of the rectangle + Area of the triangle
= 200 cm² + 60 cm²
= 260 cm²
________
Hope it helps ⚜
Each of the equal sides of an isosceles triangle is 5 inches more than twice the third side. If the perimeter of the triangle is 55 inches, find the sides of the triangle
Answers
Answer:
9 23 23
Step-by-step explanation:
Two sides are equal and are each 2x + 5 ( x = third side)
add the three sides to get 55 inches
2x + 5 + 2x+5 + x = 55
5x = 45
x = 9 so the sides are 9 and 23 and 23
Si se multiplica un numero por uno,¿que numero se obtiene?
Answers
Answer:
Si se multiplica un numero por uno, obtendras el numero original, por ejemplo 54x1 = 54, y 2x1= 2.
Step-by-step explanation:
This solid is a hemisphere with a 90° slice removed and a radius of 12
Answers
Answer:
Step-by-step explanation:
u don't know this silly question
The diagram below shows the diameter of a circular stump. Which of the following is closest to the circumference of the stump? A) 5.495 ft² B) 9.617 ft² C) 10.99 ft² D) 38.465 ft² its 3.5 ft wide
Answers
Answer:
C. 10.99
Step-by-step explanation:
i took the test
Answer:
C. 10.99
Step-by-step explanation:
usatest prep
A box of clearance clothes at a shop contains 3 red shirts and 12 black shirts. What is the probability that Ned will choose 2 red shirts randomly from the box?
12/35
1/35
2/75
3/70
Answers
The probability that Ned will choose 2 red shirts randomly from the box is 1/35.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The probability of choosing 2 red shirts randomly from the box can be calculated using the formula for probability of independent events:
P(choosing 2 red shirts) = P(choosing 1st red shirt) × P(choosing 2nd red shirt after 1st red shirt has been removed)
The probability of choosing the first red shirt is 3/15 (since there are a total of 15 shirts in the box, of which 3 are red).
After one red shirt is removed, there will be 2 red shirts and 14 shirts remaining in the box.
Therefore, the probability of choosing the second red shirt is 2/14.
P(choosing 2 red shirts) = (3/15) * (2/14) = 1/35
Therefore, the probability that Ned will choose 2 red shirts randomly from the box is 1/35.
To learn more on probability click:
https://brainly.com/question/11234923
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Which of the following is a scalar quantity, and not a vector?
velocity
temperature
acceleration
displacement
Answers
Answer:
Which of the following is a scalar quantity, and not a vector?
Temperature
Step-by-step explanation:
Force: The interaction which after applying on a body changes or try to change the state of rest or state of motion is called force.
It is a vector quantity.
Temperature: The measurement of hotness is called temperature.
It is a scalar quantity.
Scalar quantities: The physical quantities which have only magnitude and no direction are
called scalar quantities or scalars.
Examples: Mass, volume, density, time, temperature, electric current, Luminious intensity, etc. Vector quantities: The physical quantities which have both magnitude and direction and obey
the laws of vector addition are called vector quantities or vectors.
Pls help
I don’t understand
Answers
Answer:
2916 square inches
Step-by-step explanation:
Surface area of rectangular prism:
Here, area of the top of the prism is not included.
l = 24 in ; b = 20 in ; h = 16 in
Surface area = lb + 2bh + 2lh
= 24 * 20 + 2*20*16 + 2*24 *16
= 480 + 640 + 768
= 1888 sqaure inches
Surface area of triangular prism:
length = 24 in ; a = b = 16 in ; base = 20 in and height = 13 in
[tex]\sf \text{Base area=$2*\dfrac{1}{2}*base *height = base *height$}[/tex]
= 20 * 13
= 260 square inches
Surface area = length*(a +b) + base area
= 24*(16+16) + 260
= 24 * 32 + 260
= 768 + 260
= 1028 square inches
Surface area of composite figure = 1888 + 1028
= 2916 square inches
I really need help understanding when/ what situations to use sine rule and cosine rule with triangles, plssss.
thank you :)))
Answers
Answer:
See below :)
Step-by-step explanation:
If you want a missing angle or side in one pair, and you have at least one side and angle pair, use the sine rule.
If you want a remaining side, and you have the other two sides and the angle opposite the unknown side, use the cosine rule.
If you want an angle, and you have all three sides, use the cosine rule rearranged for angles.
I attached a picture to help explain better :)
What is the radius of the cone? 2 units 3 units 6 units 9 units
Answers
Answer:
where is the diameter?
Step-by-step explanation:
Answer:
Step-by-step explanation:
solve for x
please please please no links
Answers
x = 3
[tex]\bold{EXPLANATIONS:}[/tex]
Answer:
x = 5
Step-by-step explanation:
Well all you have to do is use this formula
75 + 36x -3 = 180
How did I figure that out?? Well I know that the angle next to 75 is the same as 36x-3 becuase that are alternate interior angles and 75 and 36x-3 would be a linear pair meaning that the product of the them would be 180, Thus making the formula
Now all you have to do is combine like terms:
75 -3 = 72
72 + 36x = 180
subtract 72 from both sides
72 -72 = 0
180- 72 = 108
36x = 108
divide both sides by 36
X= 5
Peter is packing toys into boxes each box holds 30 toys they are 94 toys and 3 boxes how many toys are there left
Answers
Answer:
4
Step-by-step explanation: You want to divide 94 by 30 and you 3 with a remainder of 4.
Answer: 4 toys
Step-by-step explanation:
We will multiply 3 by 30 for how many toys he can currently put into boxes.
3 * 30 = 90
Now we will subtract this from the total number of toys for our answer.
94 - 90 = 4
There are 4 toys left.
1. Select all equations that are parallel to the line 2x + 5y = 8.
A. y = x +4
B. y = -x +4
C.y-2= (x+1)
D.y-2=-(x+1)
E. 10x + 5y = 40
Answers
The line which is parallel to the line 2x + 5y =8 is [tex]y= -\frac{2}{5} x+4[/tex] .
The correct option is (B) [tex]y= -\frac{2}{5} x+4[/tex]
What is parallel line in linear equation in two variables?
If the lines are parallel, there is no solution for the pair of linear equations. If there is no solution of the given pair of linear equations, the equations are called inconsistent.
As we know the condition for two parallel line given by the equation
[tex]a_1 x+b_1y+c_1=0\\a_2x+b_2y+c_2= 0[/tex]
is:
[tex]\frac{a_1}{a_2} \; = \; \frac{b_1}{b_2}[/tex] ≠ [tex]\frac{c_1}{c_2}[/tex]
We have the given equation as 2x + 5y =8
the equation which is parallel to 2x + 5y= 8 be
B) [tex]y= -\frac{2}{5} x+4[/tex]
5y = -2x +20
2x+5y=20
So, it satisfies the condition [tex]\frac{a_1}{a_2} \; = \; \frac{b_1}{b_2}[/tex] ≠ [tex]\frac{c_1}{c_2}[/tex]
Rest of the equation aren't satisfying the condition [tex]\frac{a_1}{a_2} \; = \; \frac{b_1}{b_2}[/tex] ≠ [tex]\frac{c_1}{c_2}[/tex].
Hence the line parallel to 2x+ 5y =8 is [tex]y= -\frac{2}{5} x+4[/tex].
Learn more about the parallel line in linear equation here:
https://brainly.com/question/20847660
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How wide is a 3 ft doorway in a 1/4 inch scale drawing?
Answers
Answer:
9 inches
Step-by-step explanation:
Convert from feet to inches by multiplying by 12:
3*12 = 36
Multiply by the scale factor of 1/4:
36*1/4 = 9
9 inches
i don’t know the answer and need help
Answers
Answer:
add a screen shot
Step-by-step explanation:
Find the functional values g (-3), g (0), and g (5) for the compound function.
g (x) = 7 if x ≤ 0
1 over x if x > 0
Answers
Answer:
[tex]g(-3)=7[/tex]
[tex]g(0)=7[/tex]
[tex]g(5)=\dfrac15[/tex]
Step-by-step explanation:
[tex]g(x) =\begin{cases}7 & \text{if } x \leq 0 \\ \\\dfrac{1}{x} & \text{if } x > 0\end{cases}[/tex]
This means:
when x is equal to zero or less than zero, g(x) will always be 7.when x is more than zero, g(x) is [tex]\frac{1}{x}[/tex][tex]\implies g(-3)=7[/tex]
[tex]\implies g(0)=7[/tex]
[tex]\implies g(5)=\dfrac15[/tex]
[tex]\sf\f(x)=\grey{\begin{cases}\rm 7\quad ,x\geqslant 0\\ \rm \dfrac{1}{x}\quad ,x>0\end{cases}}[/tex]
So
-3,0 ≤05>0Hence
g(-3)=g(0)=7g(5)=1/5Find the median of:
21, 7, 32, 45, 28, 78
Answers
Arrange it in order, lowest to highest. 7, 21, 28, 32, 45, 78. Then count how many numbers there is. In your case it’s 6. So 6 divided by 2. = 3. So the third and fourth number is your median. (32+45) divided by 2 will be your answer
(4×10^-1) + (4×10^-1)
Give your anwser in standard form.
Answers
Answer:
0.8
Step-by-step explanation:
Hope this helps!
It took a car 3 days to travel 3106 miles. What was this car's average speed, in miles per hour? (round to the nearest mile per hour)
Answers
Answer:
43 mph
Step-by-step explanation:
1 day = 24 hours
3 days = 3 × 24 hours = 72 hours
The car taveled 3106 miles in 72 hours.
average speed = distance/time
average speed = (3106 miles)/(72 hours)
average speed = 43 mph
Answer: 43 mph
Explanation:
3 days is 72 hours.
R=D/T
Divide 3106 by 72
= 43 (rounded)