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3 years ago

Evaluate csc(3π/4) please show work

Mathematics

2 answers:

Nadusha1986 [10]3 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]3 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 ( $\frac{3\pi }{4}$ ) = $\frac{1}{\frac{1}{\sqrt{2} } }$ = $\sqrt{2}$

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