MHB Simplifying a trigonometric expression

AI Thread Summary
The discussion focuses on simplifying the trigonometric expression (tg 570° sin 1469°) / (ctg 495° cos 781°) by converting everything into sines and cosines and reducing the angles to their equivalents within the first cycle. The user successfully rewrites the expression to include sine and cosine values for specific angles, noting that some can be simplified directly. They emphasize the importance of knowing the values for special angles, as calculators and trigonometric tables are not allowed in their exam. The relationship between complementary angles is also highlighted, which aids in further simplification. Understanding these principles is crucial for solving the expression effectively.
Alexstrasuz1
Messages
20
Reaction score
0
(tg 570* sin 1469) / (ctg 495 * cos 781) =
Its in degrees
 
Mathematics news on Phys.org
Alexstrasuz said:
(tg 570* sin 1469) / (ctg 495 * cos 781) =
Its in degrees

I would first try to write everything in terms of sines and cosines, and then change all the angles to the corresponding angles in the first cycle (so $\displaystyle \begin{align*} 0^{\circ} \leq \theta < 360^{\circ} \end{align*}$...)
 
I did it and I got [(sin30 * sin29)/cos30]/[(cos135*cos61)/sin135]
My problem is this is for exam for university application and we can't use calculator or the sheets with trigonometric table like value of sin30 etc, I am ok with algebra since my university is focusing more on chemistry.
 
Alexstrasuz said:
I did it and I got [(sin30 * sin29)/cos30]/[(cos135*cos61)/sin135]
My problem is this is for exam for university application and we can't use calculator or the sheets with trigonometric table like value of sin30 etc, I am ok with algebra since my university is focusing more on chemistry.

Some of those values can be simplified straight away - sin(30), cos(30), cos(135) and sin(135)...
 
When I consider that the period of the tangent and cotangent functions is $180^{\circ}$ and the period of the sine and cosine functions is $360^{\circ}$, and the fact that cotangent is an odd function, I can then rewrite the given expression as:

$$-\frac{\tan\left(30^{\circ}\right)\sin\left(29^{\circ}\right)}{\cot\left(45^{\circ}\right)\cos\left(61^{\circ}\right)}$$

Now, to deal with the sine and cosine function, we see the angles $29^{\circ}$ and $61^{\circ}$ are complementary...which means the sine of one is the cosine of the other and vice versa.

As for the tangent and cotangent functions, those are special angles for which we should know the values of those functions at those angles.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Replies
2
Views
2K
Replies
3
Views
1K
Replies
28
Views
3K
Replies
3
Views
2K
Replies
5
Views
1K
Replies
11
Views
2K
Replies
1
Views
4K
Back
Top