Trigonometry - finding the appropriate angle

In summary, the least positive value of the angle A for which cosA = sinA and both are negative is 225 degrees. This can be obtained by dividing both sides by cosA and adding 180 degrees to 45 degrees, as both sin225 and cos225 are negative while sin45 and cos45 are not. The answer cannot be 45 degrees because of the precondition that sine and cosine must be negative.
  • #1
david18
49
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?
 
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  • #2
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
 
  • #3
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!
 
  • #4
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
 
  • #5
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
 
  • #6
The answer can't be 45, because of the precondition that sine and cosine must be negative.
 
  • #7
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.
 

FAQ: Trigonometry - finding the appropriate angle

What is the definition of trigonometry?

Trigonometry is a branch of mathematics that deals with the study of triangles and the relationships between their sides and angles. It is used to find missing angles or sides of a triangle when given enough information about the other angles and sides.

What is the purpose of finding the appropriate angle in trigonometry?

The purpose of finding the appropriate angle in trigonometry is to solve problems involving triangles and other geometric shapes. It is used in various fields such as engineering, physics, and astronomy to calculate distances, heights, and angles.

What are the three main trigonometric functions?

The three main trigonometric functions are sine, cosine, and tangent. These functions are used to relate the angles of a triangle to its sides. Sine is the ratio of the side opposite the angle to the hypotenuse, cosine is the ratio of the adjacent side to the hypotenuse, and tangent is the ratio of the opposite side to the adjacent side.

How do you find the appropriate angle using trigonometry?

To find the appropriate angle using trigonometry, you will need to know at least two sides of the triangle and one angle. Then you can use the appropriate trigonometric function (sine, cosine, or tangent) to calculate the missing angle.

What are some practical applications of trigonometry?

Trigonometry has many practical applications, some of which include navigation, surveying, and construction. It is also used in fields such as architecture, astronomy, and engineering to calculate heights, distances, and angles.

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