All categories

2 years ago

Evaluate csc(3π/4) please show work

Mathematics

2 answers:

Nadusha1986 [10]2 years ago

8 0

Answer:

csc(3π/4) = √2

Step-by-step explanation:

∵ csc(3π/4) = 1 ÷ sin(3π/4)

∵ ∠(3π/4) lies on the second quadrant

∴ sin(3π/4) is positive value (according to ASTC Rule)

* ASTC Rule ⇒ (All +ve in 1st quadrant , Sin +ve in 2nd , Tan +ve

in 3rd quadrant , Cos +ve in 4th quadrant)

∴ sin(3π/4) = sin(π - α) ⇒ where α is an acute angle

∴ 3π/4 = π - α ⇒ α = π - 3π/4 = π/4

∵ sin²x + cos²x = 1

∵ sin(π/4) = cos(π/4)

∴ 2sin²(π/4) = 1 ⇒ sin²(π/4) = 1/2 ⇒ sin(π/4) = √(1/2)

∴ sin (π/4) = 1/√2

∴ sin(3π/4) = 1/√2

∴ csc(3π/4) = 1 ÷ 1/√2 = 1 × √2/1 = √2

lesya [120]2 years ago

3 0

Answer:

$\sqrt{2}$

Step-by-step explanation:

Using the trigonometric identity

• csc x = $\frac{1}{sinx}$

sin( $\frac{3\pi }{4}$ ) = sin ( $\frac{\pi }{4}$ ) = $\frac{1}{\sqrt{2} }$ , hence

csc ( $\frac{3\pi }{4}$ ) = $\frac{1}{\frac{1}{\sqrt{2} } }$ = $\sqrt{2}$

You might be interested in

Solve the equation and enter the value of x below. x(8 + 9) = 34

vodomira [7]

$\huge\boxed{\mathfrak{Answer}}$

$x(8 + 9) = 34 \\ 8x + 9x = 34 \\ 17x = 34 \\ x = \frac{34}{17} \\ x = 2$

=> The answer is <u>2</u><u>.</u>

5 0

2 years ago

There are 5 boys and 6 girls participating in a singing contest. What is the likelihood that a girl will win the contest?

evablogger [386]

Answer:

add both for a total of 11

then 6/11 = .54 = 54%

5 0

3 years ago

100 POINTS

weeeeeb [17]

The blanks are as follows:

Angle addition postulate
Subtraction property of equality
Corresponding sides of similar triangles are proportional
Multiplication property of equality

8 0

2 years ago

Hey I need help with math because I don't know so what is 5 divided by 536

leonid [27]

we are asked to divide 5 over 536. Since the number we are diving by is larger than 5, the answer is a decimal number, the division can be done like this:

$5\parallel536$

We need to add zeroes to the 5 until we get a number that is largest than 536, every time we do that we also add a zero to the answer, like this:

Now, if we multiply 536 by 9 we get 4824, we subtract that from 5000, like this:

Therefore, the answer is 0.009 with a remainder of 176

6 0

1 year ago

PLEASE HELP. 15 POINTS.

Vilka [71]

Answer:

The simplest EXACT answer is $\sqrt{\frac{244}{9}$ .

A decimal form of this is approximately 5.207.

Step-by-step explanation:

Use the distance formula.

5 0

3 years ago

Read 2 more answers