Drag the slider for [math]\theta[/math] to adjust the angle. Notice the coordinates of point [math]P[/math] on the unit circle.[br]On the applet below, you have [math]\theta'[/math] as a reference angle, which is an angle between 0º and 90º.
We consider the first quadrant as the space between 0º and 90º.
1. Choose two angles in the first quadrant and register the value for their sine and cosine. [br]2. For each angle, calculate the sine and cosine of their reference angle. [br]2. Compare those values.
The sine and cosine of the angle are the same as the sine and cosine of the reference angle.
We consider the second quadrant as the space between 90º and 180º.
Choose two angles and register their values. What pattern do you see between the values of the angles chosen and their reference angles?
The angle chosen plus the reference angle equal 180º
Write down the relation you found in the previous question using math notation.
[math]\theta+\theta'=180º[/math] or [math]\theta=180º-\theta'[/math]
1. Choose two angles in the second quadrant and register their value for their sine and cosine. [br]2. For each angle, calculate the sine and cosine of their reference angle. [br]3. Compare those values.
[math]sin\left(\theta\right)=sin\left(\theta'\right)[/math][br][br][math]cos\left(\theta\right)=-cos\left(\theta'\right)[/math]
We consider the third quadrant as the space between 180º and 270º.
Choose two angles and register their values. What pattern do you see between the values of the angles chosen and their reference angles?
The angle chosen minus the reference angle is always equal to 180º
Write down the relation you found in the previous question using math notation.
[math]\theta-\theta'=180º[/math] or [math]\theta=180º+\theta'[/math]
1. Choose two angles in the second quadrant and register their value for their sine and cosine. [br]2. For each angle, calculate the sine and cosine of their reference angle. [br]3. Compare those values.
[math]sin\left(180º+\theta'\right)=-sin\left(\theta'\right)[/math][br][math]cos\left(180º+\theta'\right)=-cos\left(\theta'\right)[/math]
We consider the third quadrant as the space between 270º and 360º.
Choose two angles and register their values. What pattern do you see between the values of the angles chosen and their reference angles?
The angle chosen plus the reference angle equal 360º
Write down the relation you found in the previous question using math notation.
[math]\theta+\theta'=360º[/math] or [math]\theta=360º-\theta'[/math]
1. Choose two angles in the second quadrant and register their values for their sine and cosine. [br]2. For each angle, calculate the sine and cosine of their reference angle. [br]3. Compare those values.
[math]sin\left(360º-\theta'\right)=-sin\left(\theta'\right)[/math][br][math]cos\left(360-\theta'\right)=cos\left(\theta'\right)[/math]