What is the pattern in the values as the exponents increase?
2 answers:
Answer:
Multiply the previous value by 3.
Step-by-step explanation:
The correct pattern in the values as the exponents increase is - Multiply the previous value by 3.
We can see, that is
And in the next step, is
In the next step, is
In the last step, is
So, at each step, 3 is multiplied to the previous product/value.
Therefore, the correct answer is last option.
You might be interested in
<h2>Question:</h2>
Find the values of the sine, cosine, and tangent for ∠A
a. sin A = , cos A =
, tan A =
b. sin A = , cos A =
, tan A =
c. sin A = , cos A =
, tan A =
d. sin A = , cos A =
, tan A =
d. sin A = , cos A =
, tan A =
The triangle for the question has been attached to this response.
As shown in the triangle;
AC = 36ft
BC = 24ft
ACB = 90°
To calculate the values of the sine, cosine, and tangent of ∠A;
<em>i. First calculate the value of the missing side AB.</em>
<em>Using Pythagoras' theorem;</em>
⇒ (AB)² = (AC)² + (BC)²
<em>Substitute the values of AC and BC</em>
⇒ (AB)² = (36)² + (24)²
<em>Solve for AB</em>
⇒ (AB)² = 1296 + 576
⇒ (AB)² = 1872
⇒ AB =
⇒ AB = ft
From the values of the sides, it can be noted that the side AB is the hypotenuse of the triangle since that is the longest side with a value of ft (43.27ft).
<em>ii. Calculate the sine of ∠A (i.e sin A)</em>
The sine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the hypotenuse side of the triangle. i.e
sin Ф = -------------(i)
<em>In this case,</em>
Ф = A
opposite = 24ft (This is the opposite side to angle A)
hypotenuse = ft (This is the longest side of the triangle)
<em>Substitute these values into equation (i) as follows;</em>
sin A =
sin A =
<em>Rationalize the result by multiplying both the numerator and denominator by </em><em />
sin A =
sin A =
<em>iii. Calculate the cosine of ∠A (i.e cos A)</em>
The cosine of an angle (Ф) in a triangle is given by the ratio of the adjacent side to that angle to the hypotenuse side of the triangle. i.e
cos Ф = -------------(ii)
<em>In this case,</em>
Ф = A
adjacent = 36ft (This is the adjecent side to angle A)
hypotenuse = ft (This is the longest side of the triangle)
<em>Substitute these values into equation (ii) as follows;</em>
cos A =
cos A =
<em>Rationalize the result by multiplying both the numerator and denominator by </em><em />
cos A =
cos A =
<em>iii. Calculate the tangent of ∠A (i.e tan A)</em>
The cosine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the adjacent side of the triangle. i.e
tan Ф = -------------(iii)
<em>In this case,</em>
Ф = A
opposite = 24 ft (This is the opposite side to angle A)
adjacent = 36 ft (This is the adjacent side to angle A)
<em>Substitute these values into equation (iii) as follows;</em>
tan A =
tan A =