Given tan θ = 2 and sin θ < 0. Find cos(θ +pi/4)

Mathematics

1 answer:

Lera25 [3.4K]3 years ago

5 0

Answer:

√10 / 10

Step-by-step explanation:

tan θ > 0 and sin θ < 0, so θ is in quadrant III. That means cos θ < 0.

cos(θ + π/4)

Use angle sum formula.

cos θ cos(π/4) − sin θ sin(π/4)

½√2 cos θ − ½√2 sin θ

Factor.

½√2 cos θ (1 − tan θ)

½√2 cos θ (1 − 2)

-½√2 cos θ

Write in terms of secant.

-½√2 / sec θ

Use Pythagorean identity (remember that cos θ < 0).

-½√2 / -√(1 + tan²θ)

-½√2 / -√(1 + 2²)

½√2 / √5

√10 / 10

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What is the 7th term of the geometric sequence where a1 = -625 and a2 = 125

kykrilka [37]

Since the sequence is geometric, there is some constant $r$ such that the sequence is recursively given by

$a_n=ra_{n-1}$

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$a_n=ra_{n-1}=r^2a_{n-2}=r^3a_{n-3}=\cdots=r^{n-1}a_1=-625r^{n-1}$

You know the second term, which means you can find $r$ :

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So, the 7th term of the sequence is

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