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.

Related questions
See all questions in Applying Trig Functions to Angles of Rotation
Impact of this question
5337 views around the world
You can reuse this answer
Creative Commons License