What is #sin theta# given that #tan theta = 30/16# and #180° <= theta <=360°#?

1 Answer
EZ as pi
May 9, 2016

For # 180 <= theta <= 360,# #sin theta = -15/17#

Explanation:

By definition, Tan #theta# is # "opposite"/"adjacent"#

The sides of 30 and 16 will be in a right-angled triangle where the hypotenuse is 34. (by Pythagoras).

In this triangle, sin #theta# = #"opposite"/"hypotenuse" = 30/34 = 15/17#

However this is for an acute angle.

For # 180 <= theta <= 360,# #sin theta = -15/17#

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