trigonometry
Table of Contents
- a
- sin(x)/x
- Law of cosines
- Law of Cosines
- The Law of Cosines
- unit circle
- זהויות במעגל היחידה
- sin(ax)
- problems
- טרפז שווה שוקיים 1
sin(x)/x
Law of Cosines
In the following applets we derive the cosine law [math]c^2=a^2+b^2-2ab\cdot cos\left(\gamma\right)[/math][br]The first applet is applicable in the case [math]\gamma[/math] is an acute angle, the second for the case [math]\gamma[/math] is e an obtuse angle, and the last one for the case of a right angle.
Acute angle
After scrolling the scroll bar, and unfolding the construction, [br]use the intersecting chord theorem to obtain:[br][br][math]b\left(2a\cdot cos\left(\gamma\right)-b\right)=\left(a-c\right)\left(a+c\right)[/math][br]and therefore:[br][math]c^2=a^2+b^2-2ab\cdot cos\left(\gamma\right)[/math][br][br][br][br].
Obtuse angle
After scrolling the scroll bar, and unfolding the construction, [br]use the intersecting secant theorem to obtain:[br][math]\left(c+a\right)\left(c-a\right)=b\left(b+2a\cdot cos\left(180-\gamma\right)\right)[/math][br]and therefore:[br][math]c^2-a^2=b^2-2ab\cdot cos\left(\gamma\right)[/math][br]which is equivalent to [br][math]c^2=a^2+b^2-2ab\cdot cos\left(\gamma\right)[/math][br][br][br].
Right angle (Pythagorean theorem)
After scrolling the scroll bar, and unfolding the construction, [br]use the tangent-secant theorem to obtain:[br][math]b^2=\left(c+a\right)\left(c-a\right)[/math][br]and therefore:[br][math]c^2=a^2+b^2=a^2+b^2-2ab\cdot cos\left(90^{\circ}\right)[/math][br]
זהויות במעגל היחידה
טרפז שווה שוקיים 1
מחפשים טרפז שווה שוקיים בו הבסיס הקטן שווה ל 1.5 פעמים השוק, והבסיס הגדות שווה לאלכסון