Trigonometric function is an important part of mathematics, including sine, cosine and tangent. There are some formulas that can be converted between these functions, which are called trigonometric function exchange formulas.
Sum angle formula:
sin(a+b)= Sina cosb+cosa sinb； cos(a+b)=cosacosb-sinasinb
tan(a+b)=(tana tanb+ 1)/( 1-tana tanb)
Differential angle formula:
sin(a-b)= Sina cosb-cosa sinb； cos(a-b)=cosacosb+sinasinb
tan(a-b)=(tana tanb- 1)/( 1+tana tanb)
Double angle formula:
sin2a = 2sinacosacos2a=cos？ Sin. a； tan2a = 2 tana tan 1/( 1-tan？ answer
Half-angle formula:
sin(a/2)=√[( 1-cosa)/2]； cos(a/2)=√[( 1+cosa)/2]； tan(a/2)=√[( 1-cosa)/( 1+cosa)]
These formulas are very useful in solving trigonometric function equations or calculating trigonometric functions. For example, we can use the sum angle formula to calculate the sine, cosine and tangent of an angle, or use the double angle formula to calculate the sine and cosine of an angle. In addition, these formulas can also help us to convert units or angles when solving practical problems.
To learn trigonometric functions, we should not only master the basic definitions and properties, but also master these interchange formulas. These formulas can help us better understand and apply trigonometric functions, thus solving various practical problems.