MHB Find the exact value of each of the remaining trigonometric functions of theta

AI Thread Summary
Given that sin(θ) = 3/5, the discussion focuses on finding the remaining trigonometric functions. Since sin(θ) is positive, θ is in Quadrant I or II. Using the Pythagorean identity sin²(θ) + cos²(θ) = 1, cos(θ) can be calculated as √(1 - (3/5)²), resulting in cos(θ) = 4/5. The values for tan(θ), sec(θ), csc(θ), and cot(θ) can then be derived from sin(θ) and cos(θ). The thread emphasizes the importance of understanding trigonometric identities for solving such problems.
adrianaiha
Messages
1
Reaction score
0
sin\theta 3/5
 
Mathematics news on Phys.org
I've moved this thread to our Trigonometry forum, since this is not a calculus problem, but involves trig. instead.

I am assuming you've been given:

$$\sin(\theta)=\frac{3}{5}$$

And you are to find the values of the other 5 trig. functions as a function of $\theta$.

Since the sine of $\theta$ is positive, we know that $\theta$ is in either Quadrant I or II. To find the cosine of $\theta$, let's consider the Pythagorean identity:

$$\sin^2(\theta)+\cos^2(\theta)=1$$

Solve this for $\cos(\theta)$, and plug in the given value for $\sin(\theta)$...what do you get?
 
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