Finding Exact Values of Trig Expressions w/o Calculator

In summary, use the special triangles and trigonometric identities to solve for the exact value of sin (-pi/12) * csc (25 pi)/12 without using a calculator.
  • #1
GreenPrint
1,196
0

Homework Statement


Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator

sin (-pi/12) csc (25 pi)/12


Homework Equations


sin (negative angle) = - sin (angle)
csc theta = (sin theta)^-1 = 1/(sin theta)


The Attempt at a Solution


Ok there is obviously some sort of property of trig identies I do not know so I'm struggling here...

sin(-pi/12) csc( (25 pi)/12 ) = (- sin(pi/12) )/(sin( (25 pi)/12))
know if I'm correct I just treat them as exponents correct? so I subtract them

- sin( (pi/12) - ( (25 pi)/12 )
- sin( (-24 pi)/12 )
+ sin( (24 pi)/12
sin 2 pi = 0

OK THIS IS WRONG I put this into my calculator and i get negative one. I postulated for like two hours on how to do this. I think I figuered it out but am not sure why it works can someone please explain it to me...

ok I start out here
sin(-pi/12) csc( (25 pi)/12 ) = (- sin(pi/12) )/(sin( (25 pi)/12))


then
- sin( (pi/12) - ( (25 pi)/12 )

- sin( (24 pi)/12 )

if i just ignore the negative sign next to the 24... something here is wrong with what I'm doing HELP

- sin( (24 pi)/12 )

now I take the recipical but leave the pi on top of the angle not sure why or why i leave pi on top

- sin( (12 pi)/24

simplify

- sin( pi/2

pi/2 is ninety degrees which has the coordinates (0,1) and sense sine is equal to the y cordinate I get one but sense it's the opposite i get negative 1 as my answer which is correct

So I obviously have no idea how to really do this problem if someone could tell me how to do this that would be great. There isn't really much I can do because I'm obviously don't know some property or something here.

Thanks
 
Physics news on Phys.org
  • #2
None of your algebraic manipulations make any sense. You are just making up operations that don't exist.

Notice that Pi/12 is half of pi/6 and you know the functions for multiples of pi/6. Look at the half angle formulas instead of trying to make up your own.
 
  • #3
I have yet to have been taught these formulas yet so there must be some other way to do it
 
  • #4
Here are the two special triangles I've used in the past: http://fouss.pbworks.com/f/special triangle 3.JPG and http://fouss.pbworks.com/f/special triangle 2.JPG and recall that sin (a-b)=(sin a)(cos b)-(sin b)(cos a)

Now sin [tex]\frac{-pi}{12}[/tex] = sin ([tex]\frac{pi}{6}[/tex] - [tex]\frac{pi}{4}[/tex]) = sin [tex]\frac{pi}{6}[/tex] * cos [tex]\frac{pi}{4}[/tex] - sin [tex]\frac{pi}{4}[/tex] * cos [tex]\frac{pi}{6}[/tex]

Use the special triangles (unless you have them memorized, which you should have) and solve.

Edit: Sorry I thought you were doing two different equations. I now see that sin (-pi/12) * csc (25 pi)/12 is what you want. I guess you can do the second one and after solving it, multiple both answers.
 
Last edited by a moderator:

What is the purpose of finding exact values of trigonometric expressions without a calculator?

The purpose of finding exact values of trigonometric expressions without a calculator is to develop a deeper understanding of the relationships between the angles and sides of a right triangle, and to be able to manipulate and simplify trigonometric expressions algebraically.

What are some common techniques for finding exact values of trigonometric expressions without a calculator?

Some common techniques for finding exact values of trigonometric expressions without a calculator include using trigonometric identities, converting to special angles (such as 30-60-90 or 45-45-90 triangles), and using reference angles to find values in different quadrants.

Why is it important to be able to find exact values of trigonometric expressions without a calculator?

Being able to find exact values of trigonometric expressions without a calculator allows for more precise calculations and helps to avoid rounding errors. It also allows for a better understanding of the underlying concepts and relationships in trigonometry.

What are some common mistakes made when finding exact values of trigonometric expressions without a calculator?

Some common mistakes include using the wrong trigonometric identity, forgetting to convert to radians, and making errors in simplifying expressions. It is important to carefully check each step and be familiar with common trigonometric identities.

How can I improve my skills in finding exact values of trigonometric expressions without a calculator?

To improve your skills, you can practice using different techniques and identities, and check your answers using a calculator. It is also helpful to review the unit circle and the relationships between trigonometric functions. Working on a variety of problems and seeking clarification when needed can also improve your understanding and mastery of this skill.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
1
Views
403
Replies
4
Views
143
  • Advanced Physics Homework Help
Replies
4
Views
268
  • Precalculus Mathematics Homework Help
Replies
7
Views
1K
  • Precalculus Mathematics Homework Help
Replies
2
Views
2K
Replies
17
Views
3K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
864
  • Calculus and Beyond Homework Help
Replies
9
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
771
Back
Top