All categories

1 year ago

Find sin(x/2), cos (x/2), and tan(x/2) from the given information.

Mathematics

1 answer:

zhannawk [14.2K]1 year ago

6 0

Step-by-step explanation:

sin(x/2) = sqrt((1 - cos(x))/2)

cos(x/2) = sqrt((1 + cos(x))/2)

tan(x/2) = sin(x/2)/cos(x/2)

sin(x) = 15/17

so, we can assume the Hypotenuse of the right-angled triangle is 17, the vertical leg is 15.

via Pythagoras we get the 3rd, horizontal side :

17² = 15² + side²

289 = 225 + side²

64 = side²

side = 8

cos(x) = 8/17

sin(x/2) = sqrt((1 - 8/17)/2) = sqrt(9/34) = 3/sqrt(34) =

= 0.514495755...

cos(x/2) = sqrt((1 + 8/17)/2) = sqrt(25/34) = 5/sqrt(34) =

= 0.857492926...

tan(x/2) = 3/sqrt(34) / 5/sqrt(34) = 3/sqrt(34) × sqrt(34)/5 =

= 3/5 = 0.6

You might be interested in

The main triangular sail on a sailboat is 25 feet tall and 10 feet wide at the bottom. If the sides of another sail are proporti

lianna [129]

Answer:

Step-by-step explanation:

x - the hight of another sail

$\dfrac{8}{10}=\dfrac x{25}\\\\x=\frac8{10}\cdot25=\frac45\cdot25=4\cdot5 = 20$

4 0

3 years ago

What’s the answer need help to get good grade.

disa [49]

Answer:

3 to 7

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Foil: (x+9)(3x-4)

QveST [7]

QUESTION 1

The given binomial is;

$(x+9)(3x-4)$

First terms are multiplied: $x\times 3x=3x^2$

Outside terms are multiplied: $x\times -4=-4x$

Inside terms are multiplied: $9\times 3x=27x$

Last terms are Multiplied: $9\times -4=-36$

This gives us;

$=3x^2-4x+27x-36$

$=3x^2+23x-36$

QUESTION 2

We want to factor

$6r^5s+4r^4s^2-8r^2s$

The HCF is $2r^2s$

We factor to get;

$2r^2s(3r^3+2r^2s-4)$

QUESTION 3;

$x^2+x-2=0$

Split the middle term;

$x^2+2x-x-2=0$

Factor

$x(x+2)-1(x+2)=0$

$(x+2)(x-1)=0$

$(x+2)=0,(x-1)=0$

$x=-2,x=1$

The solutions are;

$x=-2$ and $x=1$

These are the x-intercepts of the graph of the function

$f(x)=x^2+x-2$

3 0

3 years ago

Consider the infinite geometric series 2(p-5) + 2(p-5)² + 2(p-5)³

nasty-shy [4]

10(p+3)-4(p+10)-6(p+15)

7 0

3 years ago

Patti is using beads to make anklets. Each anklet needs 9 beads, and Patti has 67 beads. How many of her beads will not be used?

Andreyy89

Answer:

Step-by-step explanation:

she can use all 63 beads because 67 divided by 9 is 7 remainder 4

8 0

2 years ago

Read 2 more answers