MHB Find cos theta and tan theta using sin theta

AI Thread Summary
Given that sin θ = 4/5, the adjacent side of the triangle is determined to be 3 using the Pythagorean theorem. Consequently, cos θ is calculated as 3/5 and tan θ as 4/3. However, it is noted that if θ is in the second quadrant, the cosine and tangent values would be negative. Therefore, both positive and negative values should be considered based on the quadrant in which the angle lies. This highlights the importance of quadrant consideration in trigonometric calculations.
mathlearn
Messages
331
Reaction score
0
If sin $$\theta$$ =$$\frac{4}{5}$$ , find cos $$\theta$$ and tan $$\theta$$

Can you help me to solve. :)

Many thanks :)
 
Mathematics news on Phys.org
Re: Find cos theta and tan theta using sin thetha

mathlearn said:
If sin $$\theta$$ =$$\frac{4}{5}$$ , find cos $$\theta$$ and tan $$\theta$$

Can you help me to solve. :)

Many thanks :)

Hey mathlearn! ;)

The sine is the opposite side divided by the hypotenuse.
What would be the length of the adjacent side, knowing we have a right triangle?
And what would then be the cosine respectively the tangent?
 
Re: Find cos theta and tan theta using sin thetha

:)

mathlearn said:
If sin $$\theta$$ =$$\frac{4}{5}$$ , find cos $$\theta$$ and tan $$\theta$$

sin $$\theta$$ = $$\frac{opposite side}{hypotenuese}$$

$$\therefore sin $$ $$\theta$$ =$$\frac{4}{5}$$

So applying Pythagoras theorem

Hypotenuse2 = opposite side 2 + adjacent side2

$$5^{2}$$ = $$4^{2}$$ + $$ adjacent side^{2}$$

$$25$$ = $$16$$ + $$ adjacent side^{2}$$

$$25$$ - $$16$$= $$ adjacent side^{2}$$

$$9$$= $$ adjacent side^{2}$$

$$\sqrt{9}$$= $$ \sqrt{adjacent side^{2}}$$

$$3$$= $$adjacent side$$

$$\therefore cos \theta$$ = $$\frac{adjacent side}{hypotenuse }$$$$\therefore cos \theta$$ = $$\frac{3}{5}$$

and

$$\therefore tan \theta$$ = $$\frac{opposite side}{adjacent side}$$

$$\therefore tan \theta$$ = $$\frac{4}{3}$$

Correct I Guess?

Many Thanks :)
 
Yep. All correct. (Nod)
 
I like Serena said:
Yep. All correct. (Nod)

Actually, it's possible that the angle could be in the second quadrant, in which case the cosine and tangent values would be negative.

Without any information about which quadrant the angle lies, you would need to write both the positive and negative answers.
 
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...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
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...
Back
Top