Find the exact value. if the expression is undefined write undefined. csc 135°

2 answers:

5 0

$\bf csc(\theta)=\cfrac{1}{sin(\theta)}\\\\
-----------------------------\\\\
csc(135^o)\implies \cfrac{1}{sin(135^o)}\implies \cfrac{1}{\frac{\sqrt{2}}{2}}\implies \cfrac{\frac{1}{1}}{\frac{\sqrt{2}}{2}}\implies \cfrac{1}{1}\cdot \cfrac{2}{\sqrt{2}}\implies \cfrac{2}{\sqrt{2}}
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\textit{now, rationalizing the denominator}
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\cfrac{2}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies \cfrac{2\sqrt{2}}{(\sqrt{2})^2}\implies \cfrac{2\sqrt{2}}{2}\implies \boxed{\sqrt{2}}$

Crazy boy [7]3 years ago

4 0

Cosec 135 = cosec 45 which is square root of 2.

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zhuklara [117]

Hey there :)

We know the distance formula is:
D = $\sqrt{(x2-x1)^2+(y2-y1)^2}$

1) Coordinates are: ( -10, -5 ) , ( 8 , 5 )
↓ ↓ ↓   ↓
x₁ y₁ x₂ y₂
We plug in the values
D = $\sqrt{(8 -(-10))^2+(5-(-5))^2}$
  ≈20.59 ≈ 20.6 (nearest tenth)

We do the same for the rest

2) Coordinates are ( 10 , 0 ) , ( -2 , 1 )
D = $\sqrt{(-2-10)^2+(1-0)^2}$
≈ 12.04 ≈ 12.0 (nearest tenth)

3) Coordinates are ( 4 , 8 ) , ( 7 , -8 )
D = $\sqrt{((7-4)^2+(-8-8)^2}$
≈ 16.27 ≈ 16.3 (nearest tenth)

4) Coordinates are ( -10, -4 ) , ( 8 , 8 )
D = $\sqrt{(8-(-10))^2+(8-(-4))^2}$
  ≈ 21.6 (nearest tenth)

5) Coordinates are ( 6 , -3 ) , ( -8 , 9 )
D = $\sqrt{(-8-6)^2 + (9-(-3))^2}$
≈ 18.4 (nearest tenth)

You can find the matching below :)