Evaluating arcsin (cos (7pi/5))

  • Thread starter Thread starter Karma
  • Start date Start date
Click For Summary
SUMMARY

The discussion focuses on evaluating the expression arcsin(cos(7π/5)). Participants clarify that to evaluate this, one can use the identity cos(θ + π/2) = -sin(θ) to simplify the expression. The key step involves recognizing that 7π/5 corresponds to an angle in the third quadrant, leading to a negative sine value. Ultimately, the evaluation requires understanding the relationship between cosine and sine in different quadrants.

PREREQUISITES
  • Understanding of trigonometric identities, specifically cos(θ + π/2) = -sin(θ)
  • Knowledge of the unit circle and angle measurements in radians
  • Familiarity with the arcsine function and its range
  • Basic calculus concepts related to trigonometric functions
NEXT STEPS
  • Study the unit circle to better understand angle positions and their corresponding sine and cosine values
  • Learn about the properties of the arcsine function and its principal values
  • Explore trigonometric identities and their applications in simplifying expressions
  • Practice evaluating trigonometric functions in different quadrants
USEFUL FOR

Students studying trigonometry, mathematics educators, and anyone seeking to improve their understanding of trigonometric evaluations and identities.

Karma
Messages
76
Reaction score
0

Homework Statement


evaluate
arcsin(cos(7pi/5))


Homework Equations


x-pi/2=7pi/5


The Attempt at a Solution


sorry don't know where to start.
 
Physics news on Phys.org
What do you mean by evaluate? What does this have to do with calculus? Could you make this a little more clear, maybe by posting what work you have, even if it is wrong?
 
cos(theta+pi/2)=-sin(theta) and then you should be able to determine what the arcsin will give you

or you could take your 7pi/5 and then add pi/2 and get -sin(theta)
 

Similar threads

Integration with Respect to x: Integral of sqrt((5-x)/x)
  • · Replies 18 ·
Replies
18
Views
4K
Prove that the integral is equal to ##\pi^2/8##
  • · Replies 105 ·
4
Replies
105
Views
7K
How Do You Solve the Inverse Function Problem Involving sin^(-1)(cos(7π/5))?
  • · Replies 3 ·
Replies
3
Views
2K
Equation of the tangent to a curve
  • · Replies 1 ·
Replies
1
Views
2K
Taylor Polynomials and Numerical Analysis
  • · Replies 2 ·
Replies
2
Views
3K
Bounds Integral of x times arcsine
  • · Replies 2 ·
Replies
2
Views
1K
Solve for Int: cos(x)=cos(17π/5)
  • · Replies 3 ·
Replies
3
Views
2K
Volume of revolution around the y-axis
  • · Replies 20 ·
Replies
20
Views
3K
Solving an Unsolvable Equation: arctan(x)+arctan(\sqrt{3}x)=\frac{7\pi}{12}
  • · Replies 6 ·
Replies
6
Views
3K
Green's Function for Linear ODE
  • · Replies 1 ·
Replies
1
Views
1K