Answer to Question #288893 in Trigonometry for Jonalyn

Question

3.)If we know the values of the sine and cosine of a and b, we can find the value of sin(A+B) by using the ____formula for sine. State the formula :

Sine(A+B)

4.)if we know the values of the sine and cosine A ana B, we can find the value of cos (A-B) by using the ____ formula for cosine. State the formula :

Cos(A-B)

5.)if we know the values of sin x and cos x, we can find the value of sin 2x by using the ____formula for sine. State the formula :sin 2x =____

6.)if we know the value of cos x and the quadrant in which x/2 lies, we can find the value of sin(x/2) by using the _____ formula for sine. State the formula:

Sin(x/2)=______

Answer 1

1. Formula sum of angles: $sin(A + B) = sin A cos B + cos A sin B$
2. Formula difference of angles: $cos(α−β)=cos(α)⋅cos(β)+sin(α)⋅sin(β)$
3. double angle formula: $sin(2x)=2sin(x)⋅cos(x)$
4. half-angle formula: $\sin(\frac{x}{2})=±\sqrt{1-cos(x)\over 2}$

+ (positive) if ${x \over 2}$ lies in quadrant | or ||

- (negative) if ${x \over 2}$   lies in quadrant ||| or |V