Trigonometry - finding the appropriate angle

Click For Summary

Homework Help Overview

The problem involves finding the least positive angle A for which both cosine and sine are equal and negative. The original poster expresses confusion due to the lack of numerical values typically provided in such problems.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the relationship between sine and cosine, with some attempting to manipulate the equation to find a solution. Questions arise regarding the conditions under which both functions are negative and the implications of the angle's quadrant.

Discussion Status

Several participants have offered insights into the problem, with one suggesting a method involving tangent and another confirming the angle of 225 degrees as a solution. However, there is also a recognition of the conditions that must be met for sine and cosine to be negative, leading to further exploration of the problem's constraints.

Contextual Notes

There is an ongoing discussion about the intervals where sine and cosine are negative, and the implications of the equation cosA = sinA. Some participants question the validity of certain angles based on the problem's requirements.

david18
Messages
49
Reaction score
0

Homework Statement



"Find the least positive value of the angle A for which:

cosA = sinA and both are negative."


Im having some trouble on this one as usually i would be given cosA=-0.2 or something but this has no figures... Any help?
 
Physics news on Phys.org
Oh i think i solved it now I divided both sides by cosA to get tan and then added 180 to 45 which gives me 225 - both sin 225 and cos 225 are negative whereas cos45 and sin45 arent
 
david18 said:

Homework Statement



"Find the least positive value of the angle A for which:

cosA = sinA and both are negative."


Im having some trouble on this one as usually i would be given cosA=-0.2 or something but this has no figures... Any help?

? there is no such number! cos(A) is negative for 90o< A< < 270. sin(A) is negative for 180o< A< 360o. cos(A) and sin(A) are both negative for any A between 180o and 270o. But there is no smallest A in that interval!
 
it says cosA=sinA meaning that sin225 is equal to whatever cos225 equals (i checked on calcualtor and they were the same.

The answer book also said 225 so I am pretty sure its right
 
david18 said:
it says cosA=sinA meaning that sin225 is equal to whatever cos225 equals (i checked on calcualtor and they were the same.

The answer book also said 225 so I am pretty sure its right

Then why is the answer not uhm...45?

which can be easily obtained by dividing by cosA
 
The answer can't be 45, because of the precondition that sine and cosine must be negative.
 
How silly of me! I completely overlooked the "sin x= cos x".

Yes, as I said before, sine and cosine are first both negative between 180 and 270 degrees. The smallest value for which sine and cosine are both negative and sin(x)= cos(x) is 180+ 45= 225 degrees.
 

Similar threads

Finding the Distance to a Building with Trigonometry
  • · Replies 4 ·
Replies
4
Views
4K
Trigonometry: finding an angle, area and length of sector of a circle
  • · Replies 2 ·
Replies
2
Views
2K
Finding area of a non right angled triangle
  • · Replies 9 ·
Replies
9
Views
4K
Finding coincident angle between 2 equally spaced sets
  • · Replies 1 ·
Replies
1
Views
2K
High School Calculating trigonometry without calculator?
  • · Replies 8 ·
Replies
8
Views
3K
What is the solution to finding d(x) without using trigonometry?
  • · Replies 2 ·
Replies
2
Views
2K
Is My Understanding of Angular Momentum and Trigonometry Correct?
  • · Replies 3 ·
Replies
3
Views
1K
Resolving angle of parallelogram in 3D space
  • · Replies 1 ·
Replies
1
Views
2K
Orbital dynamics math review for a computer simulation
  • · Replies 11 ·
Replies
11
Views
2K
Trig problem, let sinA= -3/5 wiht A in Quad. 3 find Sin2A
  • · Replies 3 ·
Replies
3
Views
4K