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Akimi4 [234]
2 years ago
8

In a right triangle, angle is an acute angle and sin angle = 4/9. Evaluate the other five trigonometric functions of angle.

Mathematics
1 answer:
kkurt [141]2 years ago
5 0

Answer:

Part 1) cos(A)=\frac{\sqrt{65}}{9}

Part 2) tan(A)=4\frac{\sqrt{65}}{65}

Part 3) cot(A)=\frac{\sqrt{65}}{4}

Part 4) sec(A)=9\frac{\sqrt{65}}{65}

Part 5) csc(A)=\frac{9}{4}

Step-by-step explanation:

Let

A------> the angle

we have that

sin(A)=\frac{4}{9}

step 1

Find the cos(A)

we know that

cos^{2}(A)+sin^{2}(A)=1

substitute the value of sin(A)

cos^{2}(A)+(\frac{4}{9})^{2}=1

cos^{2}(A)=1-(\frac{4}{9})^{2}

cos^{2}(A)=1-(\frac{16}{81})

cos^{2}(A)=(\frac{65}{81})

cos(A)=\frac{\sqrt{65}}{9}

step 2

Find the tan(A)

we know that

tan(A)=\frac{sin(A)}{cos(A)}

substitute the values

tan(A)=\frac{\frac{4}{9}}{\frac{\sqrt{65}}{9}}

tan(A)=\frac{4}{\sqrt{65}}

tan(A)=4\frac{\sqrt{65}}{65}

step 3

Find the cot(A)

we know that

cot(A)=\frac{1}{tan(A)}

we have

tan(A)=\frac{4}{\sqrt{65}}

substitute

cot(A)=\frac{1}{\frac{4}{\sqrt{65}}}

cot(A)=\frac{\sqrt{65}}{4}

step 4

Find the sec(A)

we know that

sec(A)=\frac{1}{cos(A)}

we have

cos(A)=\frac{\sqrt{65}}{9}

substitute

sec(A)=\frac{1}{\frac{\sqrt{65}}{9}}

sec(A)=\frac{9}{\sqrt{65}}

sec(A)=9\frac{\sqrt{65}}{65}

step 5

Find the csc(A)

we know that

csc(A)=\frac{1}{sin(A)}

we have

sin(A)=\frac{4}{9}

substitute the value

csc(A)=\frac{1}{\frac{4}{9}}

csc(A)=\frac{9}{4}

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Answer:

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Step-by-step explanation:

y = 2- x

\frac{5}{4}  = 2 -  \frac{3}{4}

y = 3x - 1

\frac{5}{4}  = 3 \times  \frac{3}{4}  - 1

\frac{5}{4}  =  \frac{9}{4}  -  \frac{4}{4}

Hope this helps ^-^

6 0
3 years ago
The angle by which AB turns clockwise about point B to coincide with BC is ? degrees. If from point B, a point E is drawn direct
dedylja [7]

Answer:

Step-by-step explanation:

We have the statement AB turns clockwise to coincide with BC.

= ABD + DBC

= 33.3° + 30.6°  

= 63.9°

Now we have the statement a point E is drawn directly opposite point C. B, E, and C are on the same straight line

EBC is a straight line, so sum of angles =180°

ABE + ABD + DBC = 180°

ABE + 33.3° + 30.6° = 180°

ABE + 63.9° = 180°

ABE = 180 - 63.1

ABE = 116.9° ....

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kow [346]
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3 0
2 years ago
An automobile uses 17 gal of fuel to go to 590mi. How many gallons are required to travel 870mi? (Round your answer to one decim
Valentin [98]

Answer:

Gallons = 27.95

Step-by-step explanation:

Given

Gallons : Miles = 17:590

Required

Determine the number of gallon for 870 miles

To do this, we simply substitute 870 for miles in the ratio above

So, we have:

Gallons : 870= 17:590

Convert to fraction

\frac{Gallons}{870} = \frac{17}{590}

Multiply through  by 870

870 * \frac{Gallons}{870} = \frac{17}{590}*870

Gallons = \frac{17}{590}*970

Gallons = \frac{17*970}{590}

Gallons = \frac{16490}{590}

Gallons = 27.95

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3 years ago
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NISA [10]

Answer:

B. 12 days

Step-by-step explanation:

This can be set up as an equation:
64x = 768, where x represents the days it will take to achieve 768 doughnuts.

Divide both sides by 64.

x = 12.

It will take 12 days to make an additional 768 doughnuts.

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