1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Rama09 [41]
3 years ago
14

Let sin t = a​, cos t = b​, and tan t = c. Write the expression in terms of​ a, b, and c.

Mathematics
1 answer:
maks197457 [2]3 years ago
8 0

Answer:

a+b-c

*Note c could be written as a/b

Step-by-step explanation:

-sin(-t - 8 π) + cos(-t - 2 π) + tan(-t - 5 π)

The identities I'm about to apply:

\sin(a-b)=\sin(a)\cos(b)-\sin(b)\cos(a)

\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)

\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}

Let's apply the difference identities to all three terms:

-[\sin(-t)\cos(8\pi)+\cos(-t)\sin(8\pi)]+[\cos(-t)\cos(2\pi)+\sin(-t)\sin(2\pi)]+\frac{\tan(-t)-\tan(5\pi)}{1+\tan(-t)\tan(5\pi)}

We are about to use that cos(even*pi) is 1 and sin(even*pi) is 0 so tan(odd*pi)=0:

-[\sin(-t)(1)+\cos(-t)(0)]+[\cos(-t)(1)+\sin(-t)(0)]+\frac{\tan(-t)-0}{1+\tan(-t)(0)

Cleaning up the algebra:

-[\sin(-t)]+[\cos(-t)]+\frac{\tan(-t)}{1}

Cleaning up more algebra:

-\sin(-t)+\cos(-t)+\tan(-t)

Applying that sine and tangent is odd while cosine is even.  That is,

sin(-x)=-sin(x) and tan(-x)=-tan(x) while cos(-x)=cos(x):

\sin(t)+\cos(t)-\tan(t)

Making the substitution the problem wanted us to:

a+b-c

Just for fun you could have wrote c as a/b too since tangent=sine/cosine.

You might be interested in
Determine if the product CA is defined. If the product is defined, state its dimensions. Do not calculate the product.
Troyanec [42]

ANSWER

The multiplication, CA is defined, and its dimension is 3×2

EXPLANATION

Matrix A is a 2x3 matrix.

Matrix C is a 3×2 matrix.

The product of the two matrices , CA, is defined if and only if the inner product of their dimension are the same.

CA = (2 \times 3)(3 \times 2)

The inner products are the same.

Hence the matrix multiplication, CA is defined and its dimension is the outer products.

2 \times 2

8 0
3 years ago
A cylindrical basket has a volume of 15 cubic feet. If the height of the basket is 1.5 feet, what is the area of the base of the
Eddi Din [679]

Answer:

10 ft²

Step-by-step explanation:

Recall that the volume of a uniform cylinder may be defined by the formula:

Volume = Base Area x Height

In our case we are given

Volume = 15 ft³ and Base Area = 1.5 ft

Substituting these known values into the formula gives:

Volume = Base Area x Height

15 = Base Area x 1.5

Base Area = 15 / 1.5

Base Area = 10 ft²

7 0
2 years ago
100 points and brainliest
nordsb [41]

Answer: Hello Luv......

Hope this helps. Mark me brianest please... Anna ♥

Step-by-step explanation:

Answer: -40 < T < 140

From the question, we are informed that the gas that the driver uses freezes at −40° F and evaporates at 140° F.

To get the inequality to represent the temperatures at which the gas in the truck will remain in liquid form, we should note that the temperature will be lower than 140°F but more than -40°F. This can be expressed as:

= -40 < T < 140

6 0
2 years ago
Read 2 more answers
Kenneth has 2,000$ to invest
Katarina [22]

The calculations for 2, 4, 8 year can be derived as follows,

For simple interest:

                   S.I = \frac{P*T*R}{100}

P= principle

T= Time

R= Rate

For 2 year;

            S.I = \frac{2000*2*5.6}{100}=  $224

           Amount = $2224

For 4 year;

            S.I = \frac{2000*4*5.6}{100}= $448

           Amount = $2448

For 8 year;

             S.I = \frac{2000*8*5.6}{100}= $896

           Amount = $2896

7 0
3 years ago
What us tge initial value of the linear function y= 5x - 6
Dovator [93]
X=1/5y+6/5
hope this helps!
3 0
3 years ago
Other questions:
  • The linear function f is defined by f(x)= cx + d, where c and d are constants. If f(50) = 27,000 and f(100)= 38,000, what is the
    13·1 answer
  • Clare has $150 in her bank account. She buys a bike for $200 . What is clares account balance now
    15·1 answer
  • I need help with these questions if you might not know and answer then somebody else can help thank u
    15·1 answer
  • Jamel bought 2 pounds of red apples and 3.2 pounds of green apples from the grocery store, where both kinds of apples are $1.65
    8·1 answer
  • Jennifer brought $24.75 to the base ball game. She spent $12.45 on drinks and snacks. How much money does she have left over
    5·1 answer
  • A(t+z) = 45z + 67 Solve for Z
    10·1 answer
  • Negative integers are integers less than zero is it true or false?<br> True<br> False
    13·1 answer
  • Maddie's office recycled a total of 12 kilograms of paper over 4 weeks. How many weeks will it take Maddie's office to recycle a
    13·1 answer
  • An author of a book gets 3% of the price of each book sold. He received $24,380. How many copies of the book were sold, if each
    10·1 answer
  • Pls I need help now pls help me ​
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!