This figure consists of a rectangle and a quarter circle.
1 answer:
Hello!
First you have to find the length of the side under the quarter circle
20 - 11 = 9
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Next you have to find the circumference of the quarter circle
You use the equation to find the circumference of a circle and divide the answer by 4
The equation is
r is radius
Put in 3.14 for pi and the numbers you know
2 * 3.14 * 11 = 69.08
Divide this by 4
69.08 / 4 = 17.27
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Finally you add all the values you know
20 + 2 + 17.27 + 9 + 11 + 2 = 61.27cm
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The answer is 61.27cm
Hope this helps!
First you have to find the length of the side under the quarter circle
20 - 11 = 9
------------------------------------------------------------------------------------------------------
Next you have to find the circumference of the quarter circle
You use the equation to find the circumference of a circle and divide the answer by 4
The equation is
r is radius
Put in 3.14 for pi and the numbers you know
2 * 3.14 * 11 = 69.08
Divide this by 4
69.08 / 4 = 17.27
-----------------------------------------------------------------------------------------------------
Finally you add all the values you know
20 + 2 + 17.27 + 9 + 11 + 2 = 61.27cm
------------------------------------------------------------------------------------------------------
The answer is 61.27cm
Hope this helps!
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Answer:
L.S = R.S ⇒ Proved down
Step-by-step explanation:
Let us revise some rules in trigonometry
- sin²α + cos²α = 1
- sin2α = 2 sin α cosα
- cscα = 1/sinα
To solve the question let us find the simplest form of the right side and the left side, then show that they are equal
∵ L.S = csc2α + 1
→ By using the 3rd rule above
∴ L.S = + 1
→ Change 1 to
∴ L.S = +
→ The denominators are equal, then add the numerators
∴ L.S =
∵ R. S =
∵ (sinα + cosα)² = sin²α + 2 sinα cosα + cos²α
∴ (sinα + cosα)² = sin²α + cos²α + 2 sinα cosα
→ By using the 1st rule above, equate sin²α + cos²α by 1
∴ (sinα + cosα)² = 1 + 2 sinα cosα
→ By using the 2nd rule above, equate 2 sinα cosα by sin2α
∴ (sinα + cosα)² = 1 + sin2α
→ Substitute it in the R.S above
∴ R. S =
∵ L.S = R.S
∴ csc 2α + 1 =