How do you use $csc θ = 4$ $csctheta=4$ to find $cos θ$ $costheta$ ?

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How do you use $csc θ = 4$ $csctheta=4$ to find $cos θ$ $costheta$ ?

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Answer 1 · 2017-01-15T16:58:02

$cos θ = 0.968245836$ $cos theta=0.968245836$

Explanation:

$cos e c θ = 4$ $cosec theta=4$

the opposite of $cos e c θ = sin θ$ $cosec theta= sin theta$

$sin θ = 0.25$ $sin theta= 0.25$

$theta =14°.47751219$

$= 14°28'39"$

$theta$ lies in the first quadrant where sin and cos= +

$cos theta = 0.968245836$

Answer 2 · 2017-01-15T17:13:36

Use the identities $csc(theta) = 1/sin(theta) and cos(theta) = +-sqrt(1 - sin^2(theta)$

Explanation:

Given: $csc(theta) = 4$ Find $cos(theta)$

Use the identity $csc(theta) = 1/sin(theta)$ :

$1/sin(theta) = 4$

$sin(theta) = 1/4$

Substitute $(1/4)^2$ for $sin^2(theta)$ into the identity: $cos(theta) = +-sqrt(1 - sin^2(theta)$ :

$cos(theta) = +-sqrt(1 - (1/4)^2)$

$cos(theta) = +-sqrt(1 - 1/16)$

$cos(theta) = +-sqrt(15/16)$

$cos(theta) = +-sqrt(15)/4$

Because we are not given any clue to whether $theta$ is in the first or second quadrant, we cannot determine whether the cosine is positive or negative.

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How do you use $csc θ = 4$ $csctheta=4$ to find $cos θ$ $costheta$ ?

2 Answers

Explanation:

Explanation:

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