AboutScotto Expertise Any kind of mathematics (calculus, analysis, game theory, linear approximation, finite differences, linear regression, linear programming, numerical analysis, probability, statistics, etc.).
I also have answered some questions in
Physics (mass, momentum, falling bodies),
Chemistry (charge, reactions, symbols, molecules), and
Biology.
Experience Experience in the area: I have tutored students in all areas of mathematics for over 20 years.
Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors.
Awards and Honors: I have passed Actuarial tests 100, 110, and 135.
Publications Maybe not a publication, but I have respond to well oveer 3000 questions on the PC.
That's around 2,000 in basic math and 1,000 in advanced math.
Education/Credentials I aquired well over 40 hours of upper division courses. This was well over the number that were required.
I graduated with honors in both my BS and MS degree from Oregon State University.
I was allowed to jump into a few junior level courses my sophomore year.
Awards and Honors I have been nominated as the expert of the month several times.
All of my scores right now are at least a 9.8 average (out of 10).
Past/Present Clients My past clients have been students at OSU, students at the college in South Seattle,
referals from a company, friends and aquantenances, people from my church, and people like you.
Question Hi,
My name's Veronica and I'm currently having trouble
answering these problems. I believe they have to be verified
using the pythagorean identities (i think) but my notes are
only about the sin, cos, tan, etc. I dont have notes about
these kind of problems. Please help me. Thanks.
Problems:
1) Verify: sin(theta)cos(theta)=x(square root of 25-x^2) all
over 25. where theta is an acute angle of triangle ABC withe
one side x.
2) tan^2A=x^2 all over 9-x^2
3) 4sin^2A over cosA= x^2 all over square root of 16-x^2
I will Be waiting for your answers.. Please help me I would
greatly appreciate it.. Thanks again.
Answer 1) Verify: sinΘcosΘ = x√(25 - x²)/25.
Where theta is an acute angle of triangle ABC with one side x.
It is known that for the right triangle with legs a=√(25-x²) and b=x,
the hypoteneuse is is c and a² + b² = c². Note also that the value I gave of a and b could be interchanged and the results would still be the same.
Given this, c = √(25 - x² + x²) = √25 = 5.
It is also known that sinΘ = b/c abd cosΘ = a/c.
We know that b/c = x/5 and that a/c = √(25 - x²)/5.
If they are multiplied together, the answer is x√(25 - x²)/5²,
which is the same as x√(25 - x²)/25.
2) tan^2A=x^2 all over 9-x^2
Let a=x and c=3. Given that a² + b² = c²,
we know that b=√(3²-x²)=√(9-x²).
This is because a² + b² = c² is true since a²=x² and b²=9-x².
As can be seen, when these are added together, all that is left is 9.
It can also be seen that 9=3².
3) 4sin^2A/cosA= x^2 all over square root of 16-x^2
Take a=x and c=4. Since a² + b² = c², we know that b = √(c² - a²).
With the variable a being the far side, we can say that 4sin²A = 4(a²/c²) = 4(x²/4²) = x²/4.
We also can say that cosA = √(16-x²) / 4.
Combining both of these, it can be said that
4sin²A/cosA = (x²/4) / (√(16-x²) / 4).
Since both the numerator and denominator contain /4, they cancel.
