How do you use #csctheta=4# to find #costheta#?

2 Answers
Barney V.
Jan 15, 2017

#cos theta=0.968245836#

Explanation:

#cosec theta=4#

the opposite of # cosec theta= sin theta#

#sin theta= 0.25#

#theta =14°.47751219#

#= 14°28'39"#

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

#cos theta = 0.968245836#

Douglas K.
Jan 15, 2017

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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