Trig - Addition Formula Question

In summary: So, you have(1/2)+((√3)/2-1)\tan(x)=0tan(x) = 1/2x = 30 + 180n or 210 + 180n for n = 0, 1, 2 for 0 < x < 360In summary, to solve the equation cos(x-60)=sinx, you can re-express the right-hand side as cos(90-x) and then use the trigonometric identity to simplify the equation. This results in two solutions for x in the range of 0 to 360, which are 30 and 210.
  • #1
studentxlol
40
0

Homework Statement



Solve the equation cos(x-60)=sinx

Homework Equations



cosAcosB+sinAsinB

The Attempt at a Solution



cos(x-60)=sinx
cosxcos60+sinxsin60=sinx
1/2cosx+(√3)/2sinx=sinx

How do I then solve to find x for0<x<360
 
Physics news on Phys.org
  • #2
studentxlol said:

Homework Statement



Solve the equation cos(x-60)=sinx

Homework Equations



cosAcosB+sinAsinB

The Attempt at a Solution



cos(x-60)=sinx
cosxcos60+sinxsin60=sinx
1/2cosx+(√3)/2sinx=sinx

How do I then solve to find x for0<x<360

Subtract sin(x) from both sides.

Divide by cos(x).
 
  • #3
studentxlol said:

Homework Statement



Solve the equation cos(x-60)=sinx

Homework Equations



cosAcosB+sinAsinB

The Attempt at a Solution



cos(x-60)=sinx
cosxcos60+sinxsin60=sinx
1/2cosx+(√3)/2sinx=sinx

How do I then solve to find x for0<x<360

Suggestion: don't even do it this way.

You know that sin x = cos (90-x)

So re-express RHS like that:

cos (x-60) = cos (90-x)

x-60 = 90-x + 360n (where n is an integer)

2x = 150 + 360n

x = 75 + 180n

So x = 75 or 255 for n = 0 and 1 respectively. Those are the only two solutions in the required range.
 
  • #4
studentxlol said:

Homework Statement



Solve the equation cos(x-60)=sinx

Homework Equations



cosAcosB+sinAsinB

The Attempt at a Solution



cos(x-60)=sinx
cosxcos60+sinxsin60=sinx
1/2cosx+(√3)/2sinx=sinx

How do I then solve to find x for0<x<360

SammyS said:
Subtract sin(x) from both sides.

Divide by cos(x).

Did you try what I suggested ?

What did you get ?

(1/2)cos(x)+((√3)/2-1)sin(x)=0

Now, divide by cos(x) .

[itex]\displaystyle \frac{\sin(x)}{\cos(x)}=\tan(x)[/itex] ---- Right?
 

FAQ: Trig - Addition Formula Question

What is the addition formula for trigonometric functions?

The addition formula for trigonometric functions is: sin(a + b) = sin(a)cos(b) + cos(a)sin(b) and cos(a + b) = cos(a)cos(b) - sin(a)sin(b).

How do you use the addition formula to solve trigonometric equations?

To solve trigonometric equations using the addition formula, you can substitute the values of a and b into the formula and simplify the expression to find the solution.

Can the addition formula be used for any two angles?

Yes, the addition formula can be used for any two angles, as long as they are measured in radians.

How does the addition formula relate to the unit circle?

The addition formula is derived from the relationships between the sides and angles of triangles on the unit circle. The formula helps to find the trigonometric values of the sum of two angles on the unit circle.

Are there any other trigonometric addition formulas?

Yes, there is a double angle formula which expresses sin(2a) and cos(2a) in terms of sin(a) and cos(a). There is also a half angle formula which expresses sin(a/2) and cos(a/2) in terms of sin(a) and cos(a).

Similar threads

Differential Equations: Solve the following
Replies
2
Views
1K
##\int (\sin x + 2\cos x)^3\,dx##
Replies
5
Views
2K
Derivative of a sinusoidal function
Replies
2
Views
1K
Solving DE by undetermined Coefficients
Replies
4
Views
5K
Limit of 0^0: Evaluating x^sinx
Replies
19
Views
2K
How can I determine the potential extrema on a function with a discontinuity?
Replies
4
Views
1K
How to Solve a Second Order Nonhomogeneous Differential Equation?
Replies
9
Views
2K
Method of Undetermined Coefficients
Replies
1
Views
2K
Integration using inverse trig indentities?
Replies
3
Views
1K
How to Prove the Integral of sin^7 x/(1+x^10) dx from -pi/2 to pi/2 is 0?
Replies
14
Views
1K

Hot Threads

Recent Insights

Back
Top