Find the exact value of cot(θ) for an angle θ with sin(θ) = -1/6 and with its terminal side in Quadrant III.
2 answers:
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Solution:
Given: ABCD is a Rhombus
To Prove: ΔABC≅ΔCDA
Construction: Join AC as diagonal.
Proof: ABCD is Rhombus whose sides are equal and diagonal are perpendicular bisectors. Please see attach figure.
In ΔABC and ΔCDA
AB=CD (Side of same Rhombus)
BC=DA (Side of same Rhombus)
AC=CA (Common Side of both triangle)
Therefore, ΔABC≅ΔCDA by SSS property of congruence.
Hence Proved, ΔABC≅ΔCDA
Answer:
(a) 3.5
(b) x = 4
(c) -¹/₂
(d) -¹/₂
Step-by-step explanation:
<h3><u>Part (a)</u></h3>f(1) is the value of y when x = 1.
To find the value of y from a given value of x, find the position of x on the x-axis, then trace vertically until you meet the line. Once you meet the line, trace horizontally to the y-axis to find the corresponding value of y.
Therefore, f(1) = 3.5.
<h3><u>Part (b)</u></h3>To solve f(x) = 2, find the value of x when y = 2.
To find the value of x from a given value of y, find the position of y on the y-axis, then trace horizontally until you meet the line. Once you meet the line, trace vertically to the x-axis to find the corresponding value of x.
Therefore, the solution of f(x) = 2 is x = 4.
<h3><u>Part (c)</u></h3>The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
Given interval: 2 ≤ x ≤ 4
Therefore:
- a = 2
- b = 4
The average rate of change between any interval of the given function will be the same as the graph is linear. Therefore, the average rate of change from 0 to 8 is the same as the rate found in part (c): -¹/₂.
<u>Proof</u>
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
Given interval: 0 ≤ x ≤ 8
Therefore:
- a = 0
- b = 8