MATHEMATICS HIGH SCHOOL

Given the general identity tan X =sin X/cos X , which equation relating the acute angles, A and C, of a right ∆ABC is true?A. tan A = sin A/sin C
B. cos A = tan (90-A)/sin (90-C)
C. sin C = cos A/tan C
D. cos A = tan C
E. sin C = cos (90-C)/tan A

Answers

Answer 1
Answer:

First, note that m\angle A+m\angle C=90^(\circ). Then

m\angle A=90^(\circ)-m\angle C \text{ and } m\angle C=90^(\circ)-m\angle A.

Consider all options:

A.

\tan A=(\sin A)/(\sin C)

By the definition,

\tan A=(BC)/(AB),\n \n\sin A=(BC)/(AC),\n \n\sin C=(AB)/(AC).

Now

(\sin A)/(\sin C)=((BC)/(AC))/((AB)/(AC))=(BC)/(AB)=\tan A.

Option A is true.

B.

\cos A=(\tan (90^(\circ)-A))/(\sin (90^(\circ)-C)).

By the definition,

\cos A=(AB)/(AC),\n \n\tan (90^(\circ)-A)=(\sin(90^(\circ)-A))/(\cos(90^(\circ)-A))=(\sin C)/(\cos C)=((AB)/(AC))/((BC)/(AC))=(AB)/(BC),\n \n\sin (90^(\circ)-C)=\sin A=(BC)/(AC).

Then

(\tan (90^(\circ)-A))/(\sin (90^(\circ)-C))=((AB)/(BC))/((BC)/(AC))=(AB\cdot AC)/(BC^2)\neq (AB)/(AC).

Option B is false.

3.

\sin C = (\cos A)/(\tan C).

By the definition,

\sin C=(AB)/(AC),\n \n\cos A=(AB)/(AC),\n \n\tan C=(AB)/(BC).

Now

(\cos A)/(\tan C)=((AB)/(AC))/((AB)/(BC))=(BC)/(AC)\neq \sin C.

Option C is false.

D.

\cos A=\tan C.

By the definition,

\cos A=(AB)/(AC),\n \n\tan C=(AB)/(BC).

As you can see \cos A\neq \tan C and option D is not true.

E.

\sin C = (\cos(90^(\circ)-C))/(\tan A).

By the definition,

\sin C=(AB)/(AC),\n \n\cos (90^(\circ)-C)=\cos A=(AB)/(AC),\n \n\tan A=(BC)/(AB).

Then

(\cos(90^(\circ)-C))/(\tan A)=((AB)/(AC))/((BC)/(AB))=(AB^2)/(AC\cdot BC)\neq \sin C.

This option is false.
Answer 2
Answer: The right anwer is option A.
tan A = sin A / sin C
sin C = sin A / tan A = sin A / (sin A / cos A) = cos A
sin C = cos A

Related Questions

Order numbers from least to greatest 2.8, -2 3/4, 3 1/8, -2.2
Find the sum of the following nine products: 1 × (10 – 1), 2 × (10 – 2), 3 × (10 – 3), … , 9 × (10 – 9)
Remove the parentheses and simplify the expression. 2(5k-1)-24
PLZ HELP! Question Down Below!
What are some differences and similarities between a trapezoid and a square?

How much interest will you get on $800 investment for 1 year at 6.45% ?

Answers

800 * ( 6.45 / 100 ) = 8 * 6.45 = 51.6$ ;

Find the value of 83 - [59 - (22 - 18)].
16
28
64

Answers

28 would be the correct answer to that equation

Answer:

28

Step-by-step explanation:

Using PEMDAS (order of operations) it would end up being 28

A family has 8 girls and 4 boys. A total of 2 children must be chosen to speak on the behalf of the family at a local benefit. What is the probability that 1 girl and 1 boy will be chosen?A. 2/11
B. 1/6
C. 2/33
D. 16/33

Answers

Probability is all about multiplying fractions.

The first fraction is the probability of picking a girl.. so how many of the 12 total children are girls. (8/12)

The second fraction is the probability of picking a boy.. so how many of the 11 remaining children are boys. (4/11) 

8/12 X 4/11 = 8/33 -> this isn't even an option but I'm like 10000% this is the right answer.. 

I started off this answer feeling so confident lol. good luck.
D. 16/33

because there are 28 g/g pairs, 6 b/b pairs, and 32 g/b pairs. In total 66 pairs, and of those pairs 32/66 are 1 girl and 1 boy, reduced is 16/33.

6t^3 * 6t^3

A. 12t^3
B. 12t^6
C. 36t^6
D. 36t^9

Answers

6t^3 * 6t^3
6 * 6 * t^3+3
36t^6

So, the answer is C.

6t³ * 6t³

= 6 * t³ * 6 * t³

Combine like terms

6 * 6 * t³ * t³

36 * t^6

= 36t^6


The answer is C


Good night


Which of the following are the factors of m2 – 14m + 48?A. (m – 12)(m – 4)
B. (m – 12)(m + 4)
C. (m + 6)(m + 8)
D. (m – 6)(m – 8)

Answers

The answer is D. (m-6)(m-8) hope this helped! 
D. (m-6)(m-8)

This is as...
-6 + -8 = -14
-6 * -8 = 48

You can also work out the answer by expanding the brackets.

Tammy is at the dentist's office waiting on her appointment. She notices that the 6-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle.Part 1: How many radians does the minute hand move from 1:20 to 1:55? (Hint: Find the number of degrees per minute first.)
Part 2: How far does the tip of the minute hand travel during that time?
Part 3: How many radians on the unit circle would the minute hand travel from 0° if it were to move 5π inches?
Part 4: What is the coordinate point associated with this radian measure?

Answers

PART 1:55-21=35
             35/60=.58333 
             360×.58333 =210 DEGREES
             210*pi/180 = 3.665 RADIANS

PART 2: (pi) x 2r x .58333 
              3.14 x 12 x .58333 = 21.98 in 

PART 3: 5π inches = 5 x 3.14 = 15.708 inches / 6 in radius = 2.618 radians 

PART 4: 2.618 radians * 180/pi = 150° 
             x coordinate = 6(cos 150°) = -5.196 
             y coordinate = 6(sin 150°) = 3 
             the coordinates would be (-5.196, 2)

Answer:

Part 1:

In order to find how many radians the minute hand moves from 1:20 to 1:55, we need to remember that there are 60 minutes in an hour (clock) and there are 360 degrees in the clock since the clock is a circle. After dividing 360 by 60, we find that each minute is equal to 6 degrees. After that, we can subtract the times, which tells us that there are 35 minutes between 1:20 and 1:55. Using this we can just multiply this out, to get 35 times 6, which is equal to 210 degrees. We can get our final answer by converting this into degrees. Since one 1 degree is about 0.0174, we can set up a proportion. After solving, we will get that the minutes hand moves 3.555 radians in total.

Part 2:

In order to find how much the minute hand moves, we must find the circumference, so we get c= pi times diameter. Once plugging in the 12, we see that c=37.68. 37.68 is the circumference of the entire clock and since we only need the circumference/length/distance of 35 minutes, we can set up the proportion of 37.68 in./60=x/35 and solve to get 21.98, which means 21.98 is how far the minute hand travels in 35 minutes.

Other Questions
0.1m+8-12 when m=30 and n=1/4
The Distance between two towns is 120 Kilometers. There are aproximately 8 Kilometers in 5 miles Which measurement is closest between the number of miles between these two towns? Option 1: 75 miles Option 2: 70 miles Option 3: 80 miles Option 4: 85 miles
What is the height of a rectangular prism with a base of 147cm and a volume of 1323cm
A round clock is shown below. Which of the following is closest to the number of inches around the clock