The point (16, 12) lies on the terminal side of an angle. find cos, tan, and sin

QUESTION POSTED AT 15/01/2020 - 03:11 AM

Answered by admin AT 15/01/2020 - 03:11 AM

The terminal side means that it's 16 to the right and 12 up. Which means that the triangle made from this has the sides of 16 and 12 and the hypotenuse is 20 units long. Theta, in this case, would have 16 as it's adjacent and 12 as it's opposite.
Therefore, using the Pythagorean identities:
sin(\theta) = \frac{12}{20} = \boxed{\frac{3}{5}} \\\ cos(\theta) = \frac{16}{20} = \boxed{\frac{4}{5}} \\\ tan(\theta) = \frac{12}{16} = \boxed{\frac{3}{4}} 
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Related questions

The surface areas of two similar solids are 1008cm^2 and 1372ccm^2. the volume of the larger solid is 1801cm^3 find the volume of the smaller solid round your answer to the nearest hundredth

This can be treated as a proportion problem.

Larger solid: 
Surface area = 1,372 cm²
Volume = 1,801 cm³

Smaller solid:
Surface area = 1,008cm²
Volume = ?

1,372 / 1,801 = 1008 / x
1,372 * x = 1,801 * 1008
1,372x = 1,815,408
x = 1,815,408 / 1,372
x = 1,323.18

The volume of the smaller solid is 1,323.18 cm³

ANSWERED AT 27/01/2020 - 01:38 AM


QUESTION POSTED AT 27/01/2020 - 01:38 AM

At Thursday’s basketball game, there were more than twice as many adult spectators as children. If x represents the number of adults and y represents the number of children, which inequality can be used to find the possible combinations of adults and children at the game?

Answer:

x > 2y

Step-by-step explanation:

It is given in the question that there were more than twice as many adult spectators as children.

If x represents the number of adults and y represents the number of children then inequality representing the relation will be

x > 2y

So inequality given above can be used to find the possible combinations of adults and children at the game.

ANSWERED AT 27/01/2020 - 01:31 AM


QUESTION POSTED AT 27/01/2020 - 01:31 AM

Arielle is building the wooden framework for the roof of a house. she needs the angle created by the vertical and horizontal boards of the frame to be a right angle. the height of the vertical board is 12 feet. the length of the horizontal board is 15 feet. the support beam that will connect the ends of the two boards measures 20 feet. which is true regarding the triangular frame? it is an acute triangle. about 0.8 foot needs to be removed from the 20-foot board to create a right triangle. it is an obtuse triangle. about 0.8 foot needs to be removed from the 20-foot board to create a right triangle. it is an acute triangle. about 7 feet need to be removed from the 20-foot board to create a right triangle. it is an obtuse triangle. about 7 feet need to be removed from the 20-foot board to create a right triangle.

The correct answer is:

It is an obtuse triangle; about 0.8 foot needs to be removed from the 20 foot board to create a right triangle.

Explanation:

To check the sides of the triangle to see if it forms a right triangle, we use the Pythagorean theorem:

a²+b²=c², where a and b are the legs of the triangle and c is the hypotenuse.  Using 12 and 15 for the legs, we have:

12²+15² = c²
144+225 = c²
369 = c²
√369 = √c²
19.2 = c

We need to remove 0.8 foot from the 20-foot board.

The other thing we need to know is what kind of triangle the frame will make.  Consider the angle at the top of the right triangle formed by the 15 foot board and the 12 foot board.  15 is the horizontal length and 12 is the vertical length.  15 would be across from the angle at the top, and 12 would be adjacent to this angle.  The ratio opposite/adjacent is the ratio for tangent:

tan x = (15/12)

To find the measure of x, our unknown angle, we take the inverse tangent:
tan⁻¹(tan x) = tan⁻¹(15/12)
x = tan⁻¹(15/12)
x = 51.34

This would be half of the angle at the top of the frame; this means the total angle would be 51.34+51.34= 102.68.  This makes the triangle an obtuse angle.

ANSWERED AT 27/01/2020 - 12:45 AM


QUESTION POSTED AT 27/01/2020 - 12:45 AM

What has three congruent sides?

Hey There,

An equilateral triangle has three congruent sides. All of the angles in the equilateral triangle are equal.

Hope this helps!

ANSWERED AT 27/01/2020 - 12:44 AM


QUESTION POSTED AT 27/01/2020 - 12:44 AM

Square―s = 4 1/4 ft. find the perimeter.

P=4s
P=4 x 4 1/4
P= 4ft

ANSWERED AT 27/01/2020 - 12:44 AM


QUESTION POSTED AT 27/01/2020 - 12:44 AM

Type the length of the radius in a circle if the diameter is 12 cm.

Radius is 2 x diameter. If the diameter is 12, divide by 2 which gives you 6. The radius is 6.

ANSWERED AT 27/01/2020 - 12:43 AM


QUESTION POSTED AT 27/01/2020 - 12:43 AM

Circle―r = 4 cm find the area

Are of circle = πr² = 22/7 *4*4 = 50.27cm²

ANSWERED AT 27/01/2020 - 12:43 AM


QUESTION POSTED AT 27/01/2020 - 12:43 AM

Square―s = 25 ft. find the area

A=s^2
A=25^2
A= 625ft
The area is 625ft

ANSWERED AT 27/01/2020 - 12:43 AM


QUESTION POSTED AT 27/01/2020 - 12:43 AM

Find the range of the function f(x)=4x-1 for the domain {-1,0,1,2,3}.

Answer:

Range defined as the complete set of possible values of the dependent variable,

or

The range is defined as the resulting y-values we get after substituting all the possible values of x from domain.

Given the function: f(x)=y = 4x-1

Also, x ∈Domain = {-1, 0, 1, 2, 3}

For x = -1;

y = 4(-1)-1 = -4 -1 = -5

For x = 0;

y = 4(0)-1 = 0 -1 = -1

For x = 1;

y = 4(1)-1 = 4-1 =3

For x = 2;

y = 4(2)-1 = 8-1 =7

For x = 3;

y = 4(3)-1 = 12-1 =11

Therefore, the range of the function are the set of all values of y i,e  

Range = {-5, -1, 3, 7 , 11}




ANSWERED AT 27/01/2020 - 12:42 AM


QUESTION POSTED AT 27/01/2020 - 12:42 AM

80°; 22° find the number of degrees in the third angle of the triangle

The degree of the third angle is 78.
180-(80+22)= 78

ANSWERED AT 27/01/2020 - 12:42 AM


QUESTION POSTED AT 27/01/2020 - 12:42 AM

R = 10 m find the circumference.

Multiply 10m with pi 
C=R squared times pi 
314 or 31.4 
 

ANSWERED AT 27/01/2020 - 12:42 AM


QUESTION POSTED AT 27/01/2020 - 12:42 AM

Find the slope of the graph of the following: 9x-3y=15

Answer:

Equation of line is given by:

y = mx+b; ......[1]  where m is the slope and b is the y-intercept.

Given the equation of a line: 9x-3y =15

Subtract 9x from both sides we get;

9x-3y-9x =15-9x

Simplify:

-3y =15-9x

or

-3y =-9x+15

Divide by -3 both sides we get;

y = \frac{-9x+15}{-3}

or

y = \frac{-9x}{-3} + \frac{15}{-3}

Simplify:

y = 3x - 5

On comparing with equation [1] we have;

m = 3

Therefore, the slope of the graph of the following  9x-3y =15 is, 3


ANSWERED AT 27/01/2020 - 12:42 AM


QUESTION POSTED AT 27/01/2020 - 12:42 AM

Which sequence is generated by the function f(n 1) = f(n) – 2 for f(1) = 10? (a) –10, –12, –14, –16, –18, ... (b) –2, 8, 18, 28, 38, ... (c) 8, 18, 28, 38, 48, ... (d) 10, 8, 6, 4, 2, ...

You skiped one operator.

I assume that the function is f(n+1) = f(n) - 2.

f(1) = 10
f(2) = f(1) - 2 = 10 - 2 = 8
f(3) = f(2) - 2 = 8 - 2 = 6
f(4) = f(3) - 2 = 6 - 2 = 4
f(5) = f(4) - 2 = 4 -2 = 2

So the sequence, is 10, 8, 6, 4, 2, ... [option d]

ANSWERED AT 27/01/2020 - 12:40 AM


QUESTION POSTED AT 27/01/2020 - 12:40 AM

The binomial (y − 2) is a factor of y2 − 10y 16. what is the other factor? (y − 5) (y 5) (y − 8) (y 8)

The binomial factors of the quadratic trinomial may take the forms of (y + a) and (y + b). The sum of a and b is equal to the numerical coefficient of the second term and their product should be equal to the constant. If a is equal to -2, b is equal to -8. Thus, the second factor is (y - 8).

ANSWERED AT 27/01/2020 - 12:40 AM


QUESTION POSTED AT 27/01/2020 - 12:40 AM

A customer went to a garden shop and bought some potting soil for $11.50 and 9 shrubs. the total bill was $94.75. write and solve an equation to find the price of each shrub. a. 9p 11.5p = $94.75; p = $4.62 b. 9p $11.50 = $94.75; p = $11.75 c. 9p $11.50 = $94.75; p = $9.25 d. 9(p $11.50) = $94.75; p = $5.00

Let

p---------> the price of each scrub

s----------> the price of the potting soil

T--------> total bill

we know that

 T=9p+s

in this problem

 T=\$94.75\\ s=\$11.50\\p=?

substitute the values in the formula above

 \$94.75=9p+\$11.50

solve for p

 9p=94.75-11.50

 9p=83.25

 p=9.25

therefore

the answer is the option C

 \$94.75=9p+\$11.50

 p=9.25


ANSWERED AT 27/01/2020 - 12:39 AM


QUESTION POSTED AT 27/01/2020 - 12:39 AM

Bailey writes the expression g2 14g 40 to represent the area of a planned school garden in square feet. if g = 5, what are the dimensions of the school garden? 20 feet by 2 feet 10 feet by 4 feet 12 feet by 7 feet 15 feet by 9 feet

To solve this, we must first factor g^2 + 14g + 40 to find the side lengths that are being multiplied. The factorization is (g + 4)(g + 10). Now that we have the factors, plug in 5 for g in each factor. So, the dimensions are 15 feet by 9 feet.

ANSWERED AT 27/01/2020 - 12:39 AM


QUESTION POSTED AT 27/01/2020 - 12:39 AM

What is eight increased by five? a. 12 b. 13 c. 14 d. 15

The answer is B.13.
kjjjjj

ANSWERED AT 27/01/2020 - 12:37 AM


QUESTION POSTED AT 27/01/2020 - 12:37 AM

One angle is twice another angle. the sum of the angles is 90°. how many degrees are in each angle? equation: smaller angle: larger angle:

The larger angle is 60 degrees and the smaller is 30 degrees.

ANSWERED AT 27/01/2020 - 12:34 AM


QUESTION POSTED AT 27/01/2020 - 12:34 AM

Which statements are true? check all that apply. the line x = 0 is perpendicular to the line y = –3. all lines that are parallel to the y-axis are vertical lines. all lines that are perpendicular to the x-axis have a slope of 0. the equation of the line parallel to the x-axis that passes through the point (2, –6) is x = 2. the equation of the line perpendicular to the y-axis that passes through the point (–5, 1) is y = 1.

The correct answers are:

The line x = 0 is perpendicular to the line y = –3; all lines that are parallel to the y-axis are vertical lines; the equation of the line perpendicular to the y-axis that passes through the point (–5, 1) is y = 1.

Explanation:

The line x=0 is the x-axis. The line y=-3 is a vertical line. These two will be perpendicular by definition; x=0 has a slope of 0 while y=-3 has an undefined slope. Additionally, a horizontal line will always be perpendicular to a vertical line.

In order for a line to be parallel to the y-axis, it must have the same slope as the y-axis; this means it must be a vertical line.

In order for a line to be perpendicular to the y=axis, it must be a horizontal line. The line y=1 is a horizontal line that passes through 1 on the y-axis.

ANSWERED AT 27/01/2020 - 12:34 AM


QUESTION POSTED AT 27/01/2020 - 12:34 AM

Which is a correct first step in solving the inequality –4(2x – 1) > 5 – 3x? distribute –4 to get –8x 4 > 5 – 3x. distribute –4 to get –8x – 1 > 5 – 3x. subtract 2x from both sides of the inequality. add 1 to both sides of the inequality.

Answer:

A correct first step in solving the inequality –4(2x – 1) > 5 – 3x is:

distribute –4 to get –8x +4 > 5 – 3x

Step-by-step explanation:

We have to solve the inequality:

-4(2x-1)>5-3x

Distributing -4 , we get:

-4×2x-4×(-1)>5-3x

-8x+4>5-3x

Hence, a correct first step in solving the inequality –4(2x – 1) > 5 – 3x is:

distribute –4 to get –8x +4 > 5 – 3x

ANSWERED AT 27/01/2020 - 12:31 AM


QUESTION POSTED AT 27/01/2020 - 12:31 AM

Solomon needs to justify the formula for the arc length of a sector. which expression best completes this argument? the circumference of a circle is given by the formula c=pi * d , where d is the diameter. because the diameter is twice the radius, c= 2 * pi * r. if equally sized central angles, each with a measure of n°, are drawn, the number of sectors that are formed will be equal to 360°/n° the arc length of each sector is the circumference divided by the number of sectors, or _____. therefore, the arc length of a sector of a circle with a central angle of n° is given by 2*pi*r*n/360 or pi*r*n/180 . a. 2*pi*r/270/n b. 2*pi*r/360/n c. 2*pi*r/180/n d. 2*pi*r/90/n

Answer:  The answer is (b). \dfrac{2\pi r}{\frac{360^\circ}{n^\circ}}.


Step-by-step explanation: Let us consider a circle with centre "O" and radius OA=OB=r units. We know that the circumference of a circle is 2\pi\times radius~of~the~circle, so the circumference of Circle 'C' is given by

Circumference=2\pi r.

Also, let us central angles of equal size of 'n°', the the number of sectors formed is given by

no.~of~sectors=\dfrac{360^\circ}{n^\circ}.

Now, the formula for arc length of a sector is given by

arc~length~of~of~a~sector=\dfrac{Circumference~of~the~circle}{no.~of~equally~sized~sectors}.

arc~length~of~of~a~sector=\dfrac{2\pi r}{\frac{360^\circ}{n^\circ}}.

Thus, (b) is the correct option.

ANSWERED AT 27/01/2020 - 12:31 AM


QUESTION POSTED AT 27/01/2020 - 12:31 AM

Evaluate 4!. 4 12 24

The correct answer is 24

ANSWERED AT 27/01/2020 - 12:26 AM


QUESTION POSTED AT 27/01/2020 - 12:26 AM

Find the product. (x^6)^4

Multiply 4 x 6

The answer is x^24

ANSWERED AT 27/01/2020 - 12:25 AM


QUESTION POSTED AT 27/01/2020 - 12:25 AM