The nth term of a sequence is 6 - n work out the first three terms and the 20th term of the sequence.
1 answer:
You might be interested in
Answer:
(c) 0
Step-by-step explanation:
Each of the terms in the expression represents a different transformation of a different trig function. Expressing those as the same trig function can make it easier to find the sum.
__
We can start with the identity ...
cos(x) = sin(x +π/2)
Substituting the argument of the cosine function in the given expression, we have ...
cos(π/2 -θ) = sin((π/2 -θ) +π/2) = sin(π -θ) = -sin(θ -π)
__
The first term, sin(π +θ), is a left-shift of the sine function by 1/2 cycle, so can be written ...
sin(π +θ) = -sin(θ)
The second term is the opposite of a right-shift of the sine function by 1/2 cycle, so can be written ...
cos(π/2 -θ) = -sin(θ -π) = sin(θ)
Then the sum of terms is ...
sin(π +θ) +cos(π/2 -θ) = -sin(θ) +sin(θ) = 0
The sum of the two terms is identically zero.
Answer:
x=72
Step-by-step explanation:
"An integer x is divided by an integer y, and the quotient is 24" mathematically sounds as
"The sum of these two integers is 75" has the equation
From the second equation
Substitute it into the first:
Now