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

Click For 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?
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
View full post »

Similar threads

I Finding the inverse tangent of a complex number
  • · Replies 2 ·
Replies
2
Views
3K
B Can 2(sinx) be called a 'trigonometric function'?
  • · Replies 28 ·
Replies
28
Views
3K
I Determine ## \beta ## as a function of ##\theta## linkage
  • · Replies 2 ·
Replies
2
Views
2K
B What values of m as a function of q satisfy this trigonometric equation?
  • · Replies 5 ·
Replies
5
Views
1K
I Why is it important to convert angle units when using trigonometric functions?
  • · Replies 8 ·
Replies
8
Views
2K
MHB Find All Trig Functions of Gamma Given cot(gamma)=4/3
  • · Replies 1 ·
Replies
1
Views
2K
I Question ,trigonometric identities equation and functions ?
  • · Replies 4 ·
Replies
4
Views
1K
MHB Is this Trigonometric Expression a Constant Function of x?
  • · Replies 2 ·
Replies
2
Views
1K
I Name those trigonometric functions
  • · Replies 9 ·
Replies
9
Views
2K
I Elementary Functions - What Is The Exact Definition?
  • · Replies 8 ·
Replies
8
Views
2K