Copy of Sine & Cosine of a Sum: Discovery

[color=#000000]There are 8 expressions shown off to the right. [/color]Your job is to carefully drag each expression (label) next to the segment (in the figure) whose length is given by this expression. [br][br]After doing so, please answer the 2 questions that follow.

Given what you see in your diagram, write an equivalent expression for [math]\sin\left(\alpha+\beta\right)[/math].

Hint: Opposite sides of a rectangle are congruent! [br][br][math]sin\left(\alpha+\beta\right)=cos\alpha\cdot sin\beta-sin\alpha\cdot cos\beta[/math] Hint: Opposite sides of a rectangle are congruent! [br][math]sin\left(\alpha+\beta\right)=sin\alpha\cdot cos\beta+cos\alpha\cdot sin\beta[/math] Hint: Opposite sides of a rectangle are congruent! [br][br][math]sin\left(\alpha+\beta\right)=sin\alpha\cdot sin\beta+cos\alpha\cdot cos\beta[/math]

Given what you see in your diagram, write an equivalent expression for [math]\cos\left(\alpha+\beta\right)[/math].

Hint: Opposite sides of a rectangle are congruent! [br][math]cos\left(\alpha+\beta\right)=cos\alpha\cdot cos\beta-sin\alpha\cdot sin\beta[/math] Hint: Opposite sides of a rectangle are congruent! [br][math]cos\left(\alpha+\beta\right)=sin\alpha\cdot sin\beta-cos\alpha\cdot cos\beta[/math] Hint: Opposite sides of a rectangle are congruent! [br][math]cos\left(\alpha+\beta\right)=cos\alpha\cdot sin\beta-sin\alpha\cdot cos\beta[/math]

Copy of Sine & Cosine of a Sum: Discovery

Information: Copy of Sine & Cosine of a Sum: Discovery