Question

Question #39687

Answer 1

`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`