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
Anastasy [175]
2 years ago
12

Write each of the following as a function of theta. 1.) sin(pi/4 - theta) 2.) tan(theta+30°)

Mathematics
1 answer:
Paladinen [302]2 years ago
4 0

Step-by-step explanation:

Let x represent theta.

\sin( \frac{\pi}{4} - x )

Using the angle addition trig formula,

\sin(x - y)  =  \sin(x)  \cos(y)  -  \cos(x)  \sin(y)

\sin( \frac{\pi}{4} )  \cos(x)  -  \cos( \frac{\pi}{4} )  \sin(x)

( \frac{ \sqrt{2} }{2})  \cos(x)  -  (\frac{ \sqrt{2} }{2}  )\sin(x)

Multiply one side at a time

Replace theta with x , the answer is

\frac{ \sqrt{2} \cos(x)  }{2}  -  \frac{ \sin(x) \sqrt{2}  }{2}

2. Convert 30 degrees into radian

\frac{30}{1}  \times  \frac{\pi}{180}  =  \frac{\pi}{6}

Using tangent formula,

\tan(x + y)  =  \frac{ \tan(x)  +  \tan(y) }{1 -  \tan(x) \tan(y)  }

\frac{ \tan(x) +  \tan( \frac{\pi}{6} )  }{1 -  \tan(x) \tan( \frac{\pi}{6} )  }

Tan if pi/6 is sqr root of 3/3

\frac{ \tan(x) +  ( \frac{ \sqrt{3} }{3} )  }{1 -  \tan(x)  (\frac{ \sqrt{3} }{3} )  }

Since my phone about to die if you later simplify that,

you'll get

\frac{(3 \tan(x) +  \sqrt{3} )(3 +  \sqrt{3}  \tan(x)  }{3(3 -  \tan {}^{2} (x) }

Replace theta with X.

You might be interested in
Kate wants to buy a shirt that regularly cost $30. It is on sale for 20% off. After the discount she has to pay a 6% sales tax.
enyata [817]

Answer:

25.44$

Step-by-step explanation:

20% of $30 = 6 $

Cost = 24$

Tax = 1.44$

Total cost = 25.44$

HOPE THIS HELPS

PLZZ MARK BRAINLIEST

5 0
3 years ago
Read 2 more answers
Alan buys a basket of apples on sale for $7 before tax. The sales tax is 12.5%. What is the
shtirl [24]
7.87 is what i got :) good luck!!
5 0
2 years ago
A football team lost 5 yards on each 3 plays. explain how you could use a number line to find the team's change in field positio
ollegr [7]
<span>A football team lost 5 yards on each 3 plays.
Let’s use a number line to be able to see how far in the field did they lost in 3 games.
=> 1 : 5  (1 game is to 5 yards)
=> 3 : 15 (3 games is to 15 yards )
All in all they lost 15 yards in 3 games.
pls. see attachment for more presentation.</span>



5 0
3 years ago
6 times x divided by 18
maw [93]

Answer:

\frac{6x}{18}

Step-by-step explanation:

7 0
2 years ago
Sarah said that 0.00001 is bigger than 0.001 because the first number has more digits to the right of the decimal point. Is Sara
Ivanshal [37]
No, she is wrong. 0.00001 has 4 zeros in front of the one and behind the decimal, making it 1/100000 or 1/10^5. For 0.001, there are 2 zeros in front, making it 1/1000 or 1/10^3. Since a number gets smaller as the denominator gets larger, and 10^5>10^3, 1/10^5<1/10^3
6 0
3 years ago
Other questions:
  • Aden is going to purchase sod for his backyard. How many square feet of sod will he need? There is a picture of a square with 15
    8·1 answer
  • What is the average of 17 over 15?
    13·1 answer
  • Plz plz pls help pls
    7·2 answers
  • Please answer this correctly
    10·1 answer
  • write a two-step equation that can be solved using the addition property of equality and the division property of equality.​
    6·1 answer
  • I do not know this and I need help fast this is a timed test
    11·1 answer
  • Find the sum of the roots of the quadratic x^2+7x-13=0
    14·1 answer
  • About how many more website hits were there on Saturday than on Friday?
    5·2 answers
  • Find the area of the patio
    12·1 answer
  • Are the answers 200 cm and 1052 cm? Please help!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!