Proving Trig Identities: Response

a) The equation tan(x)^2+cos(x)^2=sin(x)^2 is not a trig identity. We can verify that by putting it into the calculator, and looking at both how the graph of the rhs and lhs do not match up, and by looking at the table to see that the y1 and y2 columns don't match up.




















b) The equation 1-sec(x)^2=-tan(x)^2 is a trig identity. We can verify, but not prove this using the graph on our calculator.





















c) The reason that you can only use a calculator to verify a trig identity, and not prove it is because your calculator cannot do the algebra. While you can look at the graph to verify whether you have solved the identity, your calculator cannot show you the algebra in getting to the answer.

Without Trig, Your House Would Be Lopsided: Response

Finding the angle of elevation:
tanx=11/18

tan^-1(11/18)=x

x=31.430 degrees

So, the angle of elevation is 31.430 degrees.

Pitch, grade, and slope are all the same values on the triangle. This is also the hypotenuse value. All of these terms are showing the steepness or incline of the hypotenuse of the given triangle.

Tangent is also related to pitch, slope, and grade because you use tangent to find the angle of elevation, which is used to find the pitch. Also, when you use tangent, you are taking the tangent of the slope.

The total rise is 22 inches because, for every 18 feet horizontally, there is 11 feet vertically. Looking at the image, there are 2, 18 ft. horizontal runs, so that means that you multiply 11 x 2, to get 22 in.

The full length of the rafter line is found using the equation L=sqaure root of (1.8) squared + (22) squared. This gives us L=22.074 ft. which is the full length of the rafter line.

Err In the Direction of Kindness Response

Hi Ms. Mariner,
Thank you for sharing this blog with us! I think it is a good reminder that everybody needs to step back sometimes, especially during a time of high emotion (good or bad), and reflect on how they can be more accepting of society, and the people around them. Sometimes, we are so critical of ourselves, and try to change who we are, so that we will fit in with society. Saunders provided us with a powerful speech that invokes hope in an otherwise somewhat hopeless world. It just goes to show that you will regret many things in your lifetime, but the one thing many people regret the most is not being kind enough to others. This article is a good reminder that we all get caught up thinking about ourselves, but in the end, it is the world as a whole that matters, and not just yourself.