Question #39687

1 Answer
Peter M.
Jul 2, 2017

#sin(theta)=4/5#

Explanation:

Obtuse means that the angle is between 90˚ and 180˚.

#90<(theta)<180#

We know the following is true for any angle #theta#, so substitute in the known information and solve for #sin(theta)#:

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

#rArrsin^2(theta)=1-(-3/5)^2=1-9/25=25/25-9/25=16/25#

Take the square root of both sides:

#rArrsin(theta)=sqrt(16/25)=sqrt(16)/sqrt(25)=+-4/5#

Now, is the answer the positive or negative square root? Well, you need to know the unit circle and it's symmetry properties. You will find that #sin(theta)# is positive in the first and second quadrants. An angle between 90˚ and 180˚ corresponds to the second quadrant. Therefore, the angle is the positive root.

#sin(theta)=4/5#

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