Basic Trig Identities
Move point B so that cosA is . What is the measure of angle A?
Move point B so that cos A is . (You might have to zoom out.) What is the measure of angle A?
Play around with the above triangle and make BC very big. What happens to cos A as BC gets bigger and bigger?
What happens to the measure of angle A as BC gets bigger and bigger?
Use the above exploration to speculate as to the value of .
Use the above exploration to speculate as to the value of .
Use the above exploration to speculate as to the value of .
In the right triangle above, what is sin A?
In the right triangle above, what is cos B?
Explain why
Because sin A = cos B and B = 90 - A, we write . This is true for any angle A. This is called a cofunction identity. Write another cofunction identity based on this idea.
Above is a 3-4-5 right triangle. Verify that the Pythagorean Theorem holds.
What is sin A?
What is cos A?
Verify that the Pythagorean Theorem holds in this triangle.
What is sin A?
What is cos A?
BONUS In the above right triangle, verify the Pythagorean Identity. Do this by computing sin A and cos A and then showing that . Hint: You will need to use the relationship between a, b, and c in the right triangle.