All categories

3 years ago

Find the exact value of each of the following. In each case, show your work and explain the steps you take to find the value.

Mathematics

1 answer:

mote1985 [20]3 years ago

4 0

Answer: a) $\frac{1}{2}$

b) 1

c) 2

Step-by-step explanation:

(a) sin 17π/6

It is known that the value of sin x repeat after an interval of $2\pi\ or\ 360^{\circ}$

∴ $\sin\frac{17\pi}{6}=\sin2\frac{5\pi}{6}=\sin(2\pi+\frac{5}{6}\pi)=\sin{\frac{5}{6}\pi}=\sin(\pi-\frac{\pi}{6})=\sin(\frac{\pi}{6})=\frac{1}{2}$

[Since the value of sin x is positive in 2nd quadrant]

(b) tan 13π/4

It is known that the value of sin x repeat after an interval of $\pi\ or\ 180^{\circ}$

∴ $\tan\frac{13\pi}{4}=\tan(3\pi+\frac{\pi}{4})=\tan{\frac{\pi}{4}}=1$

(c) sec 11π/3

$\text{Since, }\sec(x)=\frac{1}{\cos x}$

$\cos(\frac{11\pi}{3})=cos(\frac{5\pi}{3}+2\pi)=\cos(\frac{5\pi}{3})=\cos(6\pi-\frac{\pi}{3})=\cos(\frac{\pi}{3})=\frac{1}{2}\\\Rightarrow\sec(\frac{11\pi}{3})=\frac{1}{\cos(\frac{11\pi}{3})}=2$

You might be interested in

Name all segments parallel to XT

butalik [34]

name two segments parallel to VU.

ST,ZY,WX

NAME TWO SEGMENTS SKEW TO SW VU,ZY,UT,XY

NAME TWO SEGMENTS SKEW TO XY SW,VZ,VS,ST,VU

8 0

3 years ago

Read 2 more answers

PLZ HELP!!!!

kherson [118]

Answer:

a=1 b=4 c=-5

Step-by-step explanation:

7 0

2 years ago

Please help !!!!!!!!!!!!

zhannawk [14.2K]

Answer:

25+40

Step-by-step explanation:

for the area of a triangle you multiple the base times the height. for the area of the square it is the length times width.

NOTE: to completely answer just add 25+40

6 0

3 years ago

Use undetermined coefficient to determine the solution of:y"-3y'+2y=2x+ex+2xex+4e3x

Kitty [74]

First check the characteristic solution: the characteristic equation for this DE is

r ² - 3r + 2 = (r - 2) (r - 1) = 0

with roots r = 2 and r = 1, so the characteristic solution is

y (char.) = C₁ exp(2x) + C₂ exp(x)

For the ansatz particular solution, we might first try

y (part.) = (ax + b) + (cx + d) exp(x) + e exp(3x)

where ax + b corresponds to the 2x term on the right side, (cx + d) exp(x) corresponds to (1 + 2x) exp(x), and e exp(3x) corresponds to 4 exp(3x).

However, exp(x) is already accounted for in the characteristic solution, we multiply the second group by x :

y (part.) = (ax + b) + (cx ² + dx) exp(x) + e exp(3x)

Now take the derivatives of y (part.), substitute them into the DE, and solve for the coefficients.

y' (part.) = a + (2cx + d) exp(x) + (cx ² + dx) exp(x) + 3e exp(3x)

… = a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)

y'' (part.) = (2cx + 2c + d) exp(x) + (cx ² + (2c + d)x + d) exp(x) + 9e exp(3x)

… = (cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

Substituting every relevant expression and simplifying reduces the equation to

(cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

… - 3 [a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)]

… +2 [(ax + b) + (cx ² + dx) exp(x) + e exp(3x)]

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

… … …

2ax - 3a + 2b + (-2cx + 2c - d) exp(x) + 2e exp(3x)

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

Then, equating coefficients of corresponding terms on both sides, we have the system of equations,

x : 2a = 2

1 : -3a + 2b = 0

exp(x) : 2c - d = 1

x exp(x) : -2c = 2

exp(3x) : 2e = 4

Solving the system gives

a = 1, b = 3/2, c = -1, d = -3, e = 2

Then the general solution to the DE is

y(x) = C₁ exp(2x) + C₂ exp(x) + x + 3/2 - (x ² + 3x) exp(x) + 2 exp(3x)

4 0

3 years ago

Explain how you can use base-ten blocks or as a decimal models to find 3.15 divided by 3. Include pictures to support your expla

AlladinOne [14]

You have to turn the number or ratio and simplified the number and put it in to the chart like the norm number

.

5 0

3 years ago