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
Komok [63]
3 years ago
13

Match the identities to their values taking these conditions into consideration sinx=sqrt2 /2 cosy=-1/2 angle x is in the first

quadrant and angle y is in the second quadrant. Information provided in the picture. PLEASE HELP

Mathematics
1 answer:
BaLLatris [955]3 years ago
6 0

Answer:

\cos(x+y) goes with -\frac{\sqrt{6}+\sqrt{2}}{4}

\sin(x+y) goes with \frac{\sqrt{6}-\sqrt{2}}{4}

\tan(x+y) goes with \sqrt{3}-2

Step-by-step explanation:

\cos(x+y)

\cos(x)\cos(y)-\sin(x)\sin(y) by the addition identity for cosine.

We are given:

\sin(x)=\frac{\sqrt{2}}{2} which if we look at the unit circle we should see

\cos(x)=\frac{\sqrt{2}}{2}.

We are also given:

\cos(y)=\frac{-1}{2} which if we look the unit circle we should see

\sin(y)=\frac{\sqrt{3}}{2}.

Apply both of these given to:

\cos(x+y)

\cos(x)\cos(y)-\sin(x)\sin(y) by the addition identity for cosine.

\frac{\sqrt{2}}{2}\frac{-1}{2}-\frac{\sqrt{2}}{2}\frac{\sqrt{3}}{2}

\frac{-\sqrt{2}}{4}-\frac{\sqrt{6}}{4}

\frac{-\sqrt{2}-\sqrt{6}}{4}

-\frac{\sqrt{6}+\sqrt{2}}{4}

Apply both of the givens to:

\sin(x+y)

\sin(x)\cos(y)+\sin(y)\cos(x) by addition identity for sine.

\frac{\sqrt{2}}{2}\frac{-1}{2}+\frac{\sqrt{3}}{2}\frac{\sqrt{2}}{2}

\frac{-\sqrt{2}+\sqrt{6}}{4}

\frac{\sqrt{6}-\sqrt{2}}{4}

Now I'm going to apply what 2 things we got previously to:

\tan(x+y)

\frac{\sin(x+y)}{\cos(x+y)} by quotient identity for tangent

\frac{\sqrt{6}-\sqrt{2}}{-(\sqrt{6}+\sqrt{2})}

-\frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}+\sqrt{2}}

Multiply top and bottom by bottom's conjugate.

When you multiply conjugates you just have to multiply first and last.

That is if you have something like (a-b)(a+b) then this is equal to a^2-b^2.

-\frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}+\sqrt{2}} \cdot \frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}-\sqrt{2}}

-\frac{6-\sqrt{2}\sqrt{6}-\sqrt{2}\sqrt{6}+2}{6-2}

-\frac{8-2\sqrt{12}}{4}

There is a perfect square in 12, 4.

-\frac{8-2\sqrt{4}\sqrt{3}}{4}

-\frac{8-2(2)\sqrt{3}}{4}

-\frac{8-4\sqrt{3}}{4}

Divide top and bottom by 4 to reduce fraction:

-\frac{2-\sqrt{3}}{1}

-(2-\sqrt{3})

Distribute:

\sqrt{3}-2

You might be interested in
Which figure contains an angle bisector?
Anastaziya [24]

Answer: Figure 2.

Step-by-step explanation:

Suppose that we have an angle with measure ∠M, a bisector would be a line that divides this angle in two equal parts, such that each new angle has measures (∠M)/2

Then the correct option will be the one that has two equal angles.

In figure 2, we can see that RP divides the angle SRQ in two angles 52°, then RP is the bisector of the angle.

Then the correct option is figure 2.

6 0
2 years ago
Choose 3 values that would make this inequality true. 9 - n ≥ 4
Alenkasestr [34]

Answer: Could be 0,1,2,3,4,5

Step-by-step explanation: 9-n has to be greater or equal to four. 9 minus 4 is five. So all of the answers must be positive numbers that are less than five.

6 0
2 years ago
Use the graph of the function to find the domain of f. (Enter your answer using interval notation.).
Ulleksa [173]

Answer:

Domain: (-∞,0) ∪ [0,∞)

Range: [-3,∞)

f(0) = -3

6 0
3 years ago
If John has an apple, an orange, a pear, a banana, and a kiwi at home and he wants to bring two fruits for lunch, how many diffe
SVEN [57.7K]

Answer:

10

Step-by-step explanation:

5 choose 2 is 5x4/2, which is 20/2, which is 10.

5 0
3 years ago
2+2..................​
Nana76 [90]

Answer:

4..............21...........

4 0
3 years ago
Other questions:
  • If they immediately ran in opposite directions with speeds of 180 feet per minute and 120 feet per minute respectively, how many
    13·2 answers
  • What is the slope of y = -4?
    13·1 answer
  • Need so help on all of this
    5·1 answer
  • Helpppppp me plssss ​
    7·1 answer
  • Maritza is buying wheels for her skateboard shop. She ordered a total of 92 wheels. If wheels come in packages of 4, how many pa
    13·2 answers
  • Which is one of the transformations applied to the graph of <img src="https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2" id="TexFormula1"
    5·1 answer
  • Please please help asap!!
    10·1 answer
  • Find the value of x please
    8·1 answer
  • 1. An interior design company needs materials for a new job. They need to purchase four doors. Each door costs $185.95. They als
    7·1 answer
  • Who does e.d.e.n.u.i.t.y and needs help catching up?/ I'm free to help... only up to 8th grade though...
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!