Question

Evaluate the following equation.

cos^-1 (cos(-pi/6))

and

sin(tan^-1(4/3))

Answer 1

Do you still need help with this? I started answering hours ago then had to break away to go to my daughter's HS graduation! But if you need help still, I'd love to do it! This looks to me like you are ultimately solving for the inverse cos in the first one and the sin of the second one, right? Like I always tell my math students, it is easier for the mind to deal with degrees as opposed to radians, so let's convert this to degrees. And keep in mind, as well, that this a negative angle measure so instead of going counterclockwise, it goes clockwise. Ok, so that is a negative 30 degree angle, located in the 4th quadrant. The 30 degree angle is part of a special right triangle. Let's look at it
The cos of that 30 degree angle is the side adjacent to the angle over the hypotenuse, so it's \[\frac{ \sqrt{3} }{ 2 }\]Actually that is a \[-\frac{ \sqrt{3} }{ 2 }\]Now divide this out to get a decimal. -.866025. Take the inverse cosine of this on your calculator in degrees and get a degree measure of 150 degrees. In radians, that would be\[\frac{ 5\pi }{ 6 }\]If you don't know how to convert back and forth between radians and degrees, let me know. Now for the next one. Divide the 4 by the 3 to start. That number is 1.3333...Take the inverse tangent of that in degrees to get 53.13 degrees. Now take the sin of 53.13 and that's .7999999. Anything I did that you don't understand, feel free to ask!