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