The domain is , where n is an integer.
- This is because cot x = 1/tan(x), and if tan x = 0, then the fraction is undefined.
The range is <u>all real numbers</u>.
You know that for any , neither sin nor cos can be greater than 1. how can you explain this using the unit circle definitions of
1 answer:
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Answer:
a = √11 and b = 6
Step-by-step explanation:
Refer to attached picture for reference
for an right triangle with angle θ
we are given
cos θ = 5/6 = length of adjacent side / length of hypotenuse
hence
adjacent length = 5 units
hypotenuse length = 6 units
the missing side is the "opposite" length which we can find with the Pythagorean equation. in our case:
hypotenuse ² = adjacent ² + opposite² (rearrange)
opposite ² = hypotenuse ² - adjacent ²
opposite ² = 6² - 5²
opposite = √ (6²-5²) = √11
sin θ = opposite length / hypotenuse (substitute values above)
sin θ = √11 / 6
hence a = √11 and b = 6
Answer:
Length, l = 11 ft.
Width, w = 9 ft.
Step-by-step explanation:
From the given data, the area of the rectangle = 99 ft².
Area of the rectangle = Length, l X Width, w
Here, Length, l = 7 more than twice the width
⇒ Length, l = 7 + 2w
Therefore, Area, A = 99 = (7 + 2w)w
⇒ 99 = 7w + 2w²
⇒ 2w² + 7w - 99 = 0
Solve the Quadratic equation using the formula: x = for the quadratic equation ax² + bx + c = 0.
Therefore, w =
Since, we get:
This gives two values of 'w', viz., w = ,
⇒ w = , -9.
We take the integer values.
If w = -9, then l = 2(-9) + 7
⇒ l = - 18 + 7 = - 11
Therefore, the length, l of the rectangle = - 11 ft.
and the width, w of the rectangle = - 9 ft.
Hence, the answer.