An angle in standard position such that sinÈ = 5/13. Determine the possible values of È, to the nearest degree.

Answer: I got 23°. (How do I get the second one?)

SinTheta=sin(180-Theta)

The sine curve is symmetrical about 90 degrees.

So sin(x) has the same value as sin(180-x).

Review of the unit circle will certainly help as well.

Thank you

You're welcome! :)

To find the second possible value of È, we need to consider that the sine function is positive in both the first and second quadrants. Since we already found one value in the first quadrant, we need to find the corresponding angle in the second quadrant that has the same sine value.

To do this, we can use the inverse sine function (also known as arcsine or sin^(-1)). The inverse sine function will give us angles that have the same sine value as the given ratio.

Let's calculate the inverse sine of 5/13 to find the first possible angle in the first quadrant:

sin^(-1)(5/13) ≈ 0.3946 radians ≈ 22.62 degrees (rounded to two decimal places).

Now, to find the second angle in the second quadrant, we can subtract the angle we found in the first quadrant from 180 degrees since the second quadrant spans from 90 degrees to 180 degrees:

180 degrees - 22.62 degrees ≈ 157.38 degrees (rounded to two decimal places).

Therefore, the second possible value of È, to the nearest degree, is 157 degrees.