AboutPaul Klarreich Expertise All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions.
I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.
Experience I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.
Question Hi myy 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 Questioner: Veronica
Country: Philippines
Category: Calculus
Private: No
Subject: TRIGONOMETRY (trigonometric functions) but not sure if this is also included with it
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)
>> and the quotient identities and the reciprocal identities, etc. -- you have to know them all.
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.
..........................................................
Hi, Veronica,
I think you have left out some information in each of these, such as a 'beginning' value of one of the functions or the dimensions of the triangle.
1) Verify: sin(t) cos(t)= x sqrt(25-x^2) /25.
over 25. where theta is an acute angle of triangle ABC withe
one side x.
YOU MEAN with one side x that is opposite angle t, and the hypotenuse equal to 5, don't you. Your triangle looks like this:
B
/|
/ |
/ |
/ |
5 / | x
/ |
/ |
/ |
/ t |
A---------+C
sqrt(25 - x^2)
and you got AC by using the Pythagorean Theorem. Now it is an easy matter to write:
x
sin t = -------
5
x
cos t = --------------
sqrt(25 - x^2)
and now you can verify your identity.
I think that you can now go back and handle the other problems. You will supply the missing information and do them the same way.
