Ask question

Ask question

All categories

mihalych1998 [28]

2 years ago

15

Trigonometry: If f(x)= 2sinx + cosx using exact values find f (120 degrees). if possible show steps.

1 answer:

Arada [10]2 years ago

3 0

Answer: f(120°) = (√3) + 1/2

Step-by-step explanation:

i will solve it with notable relations, because using a calculator is cutting steps.

f(120°) = 2*sin(120°) + cos(120°)

=2*sin(90° + 30°) + cos(90° + 30°)

here we can use the relations

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

sin(a + b) = cos(a)*sin(b) + cos(b)*sin(a)

then we have

f(120°) = 2*( cos(90°)*sin(30°) + cos(30°)*sin(90°)) + cos(90°)*cos(30°) - sin(90°)*sin(30°)

and

cos(90°) = 0

sin(90°) = 1

cos(30°) = (√3)/2

sin(30°) = 1/2

We replace those values in the equation and get:

f(120°) = 2*( 0 + (√3)/2) + 0 + 1/2 = (√3) + 1/2

You might be interested in

Given the three vertices W(−1, 4), X(−3, −2), and Y(3, −4), what are the coordinates of Z that make quadrilateral WXYZ a square?

prohojiy [21]

Answer:

I don't see how the three existing points could ever become a square with the addition of a foiurth point.

Step-by-step explanation:

See the attached image.

A square would require that all angles be 90 degrees. The given points are the top three points on the graph. If we enter the two equations that intersect these points (blue and black lines), we can see that the angle on top is not 90 degrees. I can't see that this could ever be a square with a fourth point, z. I did find a value for z that make the four points a parallelogram.

5 0

2 years ago

Isaac downloaded 7 ringtones. Each polyphonic ringtone costs $3.25, and each standard ringtone costs $1.50. If he spends a total

anzhelika [568]

Answer:

$6\ polyphonic\ ringtones$ and $1\ standard\ ringtone$

Step-by-step explanation:

Let

x -----> the number of polyphonic ringtones

y ----> the number of standard ringtones

we know that

$x+y=7$

$x=7-y$ -----> equation A

$3.25x+1.50y=21$ -----> equation B

Solve the system of equations by substitution

Substitute equation A in equation B and solve for y

$3.25(7-y)+1.50y=21$

$22.75-3.25y+1.50y=21$

$3.25y-1.50y=22.75-21$

$1.75y=1.75$

$y=1\ standard\ ringtones$

Find the value of x

$x=7-1=6\ polyphonic\ ringtones$

6 0

2 years ago

Read 2 more answers

Write and solve a word problem that matches the diagram shown

lapo4ka [179]

Please include the diagram

6 0

2 years ago

Delaney bought a crate for her puppy when it was 3 months old. The crate is in the shape of a rectangular prism. Since the puppy

Alika [10]

Answer:

The volume of the new crate is exactly 174.4% of the old crate.

Step-by-step explanation:

Volume of a rectangular prism:

The volume of a rectangular prism of dimensions x, y and z is given by:

$V = xyz$

She decided that the dimensions of the new crate needs to be increased by 40% of the original length.

Each dimension is increased by 40%, which means that each is multiplied by 1 + 0.4 = 1.4. So

$V = 1.4x(1.4y)(1.4z) = (1.4)^3(xyz) = 2.744(xyz)$

Percentage:

The new volume is 2.744 the original volume. Considering the original volume is 100% = 1, it increased by 2.744 - 1 = 1.744 = 1.744*100% = 174.4%.

The volume of the new crate is exactly 174.4% of the old crate.

7 0

2 years ago

How do you do this?<br> Because i don't know how to do it :>

Sindrei [870]

Answer:

£ 7.95

Step-by-step explanation:

Let the total money = £ x

Money spend on drinks and cake = 1.45 + 1.20 = £ 2.65

Money left with her = (2/3) of x

So, money spend = (1/3) of x

$\dfrac{1}{3}*x= 2.65\\\\\\x=2.65*3\\\\$

x = £ 7.95

7 0

1 year ago