BallerAlert1644
31.01.2020 •
Mathematics
Can anybody show me how to do this half angle identity problem step by step? i always seem to be missing something
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Ответ:
Step-by-step explanation:
It is given that θ is between 270° and 360°, which means that θ is located in Quadrant IV ⇒ (x > 0, y < 0). Furthermore, the half-angle will be between 135° and 180°, which means the half-angle is in Quadrant II ⇒
It is given that sin θ = ⇒ y = -7 & hyp = 25
Use Pythagorean Theorem to find "x":
x² + y² = hyp²
x² + (-7)² = 25²
x² + 49 = 625
x² = 576
x = 24
Use the "x" and "hyp" values to find cos θ:
Lastly, input cos θ into the half angle formula:
Reminder: We previously determined that the half-angle will be negative.
Ответ:
no
Step-by-step explanation:
Establish the nth term formula
There is a common difference d between consecutive terms, that is
d = - 5 - (- 9) = - 1 - (- 5) = 3 - (- 1) = 7 - 3 = 4
This indicates the sequence is arithmetic with nth term
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 9 and d = 4 , then
= - 9 + 4(n - 1) = - 9 + 4n - 4 = 4n - 13
Equate 4n - 13 to 301
4n - 13 = 301 ( add 13 to both sides )
4n = 314 ( divide both sides by 4 )
n = 78.5
Since n is not an integer then 301 is not in the sequence