Given that cos t=(3/4) and that P(t) is a point in the fourth quadrant, what is sin (t)?

1 Answer
Douglas K.
Apr 5, 2018

#sin(theta) = -sqrt7/4#

Explanation:

Start with the identity:

#sin(theta) = +-sqrt(1-cos^2(theta))#

We are told that #theta# is in the fourth quadrant and we know that the sine function is negative in the fourth quadrant, therefore, we shall choose the negative case of the identity:

#sin(theta) = -sqrt(1-cos^2(theta))#

Substitute #cos^2(theta) = (3/4)^2#:

#sin(theta) = -sqrt(1-(3/4)^2)#

#sin(theta) = -sqrt(16/16-9/16)#

#sin(theta) = -sqrt(7/16)#

#sin(theta) = -sqrt7/4#

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