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
= Solving a word problem with two unknowns using a linear... A washer and a dryer cost $650 combined. The washer costs $100 less
nikdorinn [45]

Answer:

Washer 225

Dryer 425

.....

7 0
2 years ago
Find the missing side lengths
Mashcka [7]

Answer:

y = 9√3

x = 18

Step-by-step explanation:

taking 30 as reference angle

b = y

p = 9

h = x

so

tan30 = p/b

1/√3 = 9/b

or, b = 9√3

so

h^2 = p^2 + b^2\\x^2 = 9^2 + y^2\\or, x^2 = 81 + (9\sqrt{3} )^2\\or, x^2 = 81 + 243\\or, x ^2 = 324\\or, x =\sqrt{324} \\\\so x = 18

7 0
3 years ago
A bag of trail mix weighs 2 lb. By weight, 20% of the bag is oats. How many pounds is the oats portion of the trail mix? (a) Wri
posledela
Answer: 0.4 pounds of the trail mix is oats.

To find the answer, you can set up a proportion. We can use the percent proportion below.

part/whole = percent/100

x/2 = 20/100

To solve this you cross multiply and divide.

100x = 40
x = 0.4
3 0
3 years ago
Ken, the camp cook, makes 3 meals for every camper. The
dalvyx [7]

Answer: number of meals on the left side then number of campers on the bottom

Step-by-step explanation:

A p e x and it says 3 meals for every camper it never said how long so it’s not going to be so the graphs with day in it next you can’t put campers on the side cause if you don’t have enough meals for everyone you ant goin keep the campers happy so that’s how I got my answer sorry if that was confusing brainless please

3 0
2 years ago
Read 2 more answers
Solve x2 - 4x + 1 = 0.<br> x = 2+ 21-25<br> X = 4+<br> X = 2+ 3<br> x = -2+
adelina 88 [10]
I think the answer is this
2x-4x+1=0
Combine like terms
-2x+1=0
Subtract 1 both sides
-2x=-1
Divide by -2 both sides
x=-1/2
5 0
2 years ago
Other questions:
  • Q equal 1/2 p plus 15 solve for p
    5·1 answer
  • Is 32.725 greater or lesser then 32.735
    7·1 answer
  • What is the measurement of an interior angle of a regular triangle
    9·1 answer
  • Graph each system. The find the solution from the graph. I don't understand this I've had it for 2 weeks now and never turned it
    13·1 answer
  • The speed of the current in a stream is 2 mi/hr. It takes a canoeist 120 minutes longer to paddle 22.5 miles upstream than to pa
    9·1 answer
  • Help ASAP!!!!<br><br> I don’t know what I’m doing
    13·1 answer
  • Please help thank u so much
    8·2 answers
  • Lement3
    15·1 answer
  • A car travels 200 miles on 8 gallons of gas. How far can it travel on 20 gallon
    5·2 answers
  • What is the average rate of change for this quadratic function for the interval
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!