Pythagorean Steps

What could be our first strategy to simplify the right side?

• Rewrite into sines and cosines

• Combine fractions

• factor common factor

• multiply by the conjugate

• Use a Pythagorean Identity

Put the steps in the correct order to verify that the two sides are equal: \frac{\sec x}{\sin x}-\frac{\sin x}{\cos x}=\frac{\cos x}{\sin x}

• Put in terms of sine and cosine (reciprocal ID) 

• Simplify (cancel)

• Simplify/cancel on top only

• Replace using Pythagorean ID

•  Get a common denominator

Put the steps in the correct order to verify that the two sides are equal: \frac{\csc x}{\cos x}-\frac{\cos x}{\sin x}=\frac{\sin x}{\cos x}

•  Get a common denominator

• Put in terms of sine and cosine (reciprocal ID) 

• Replace using Pythagorean ID

• Simplify (cancel)

• Simplify/cancel on top only

What could be our first strategy to simplify the left side?

• Rewrite into sines and cosines

• separate fractions

• factor common factor

• multiply by the conjugate

• Use a Pythagorean Identity

Find the missing length indicated. Leave your answer in simplest radical form.

• 64

• 12

• 9

• 100

The Pythagorean Theorem ONLY works on which type of triangle? 

• Obtuse

• Right

• Acute

• Isosceles

What is side c called?

• Leg

• Hypotenuse

What are sides a and b called?

• Legs

• Hypotenuse

What is the formula for the Pythagorean Theorem if sides a and b are legs and side c is the hypotenuse of a right triangle?

Find the length of the missing side

• 17

• 15

• 22

• 13