TRIGONOMETRY(RIGHT TRIANGLES)

WHY DO WE NEED TRIGONOMETRY?

• IN PHYSICS, WE WILL OFTEN BE USING RIGHT TRIANGLES IN DIAGRAMS. TRIGONOMETRY LETS US FIND MISSING SIDE LENGTHS AND ANGLES OF RIGHT TRIANGLES.

• IS IT NOT THAT HARD TO DO THE COMPUTATIONS WE WILL NEED FOR THIS COURSE, SO LET’S GET TO IT!

THE RIGHT TRIANGLE

THE PYTHAGOREAN THEOREM

• FOR RIGHT TRIANGLES ONLY!

• USED WHEN WE KNOW THE LENGTHS OF ANY 2 SIDES OF A RIGHT TRIANGLE AND WE NEED TO KNOW THE THIRD LENGTH.

• FORMULA:

…WHERE A AND B ARE THE LEGS AND C IS THE HYPOTENUSE.

TRIGONOMETRY

WHEN WE KNOW ONLY ONE SIDE AND ONE ANGLE OF A RIGHT TRIANGLE

OR

WHEN WE NEED TO FIND AN ANGLE OF A RIGHT TRIANGLE

WE WILL USE THE TRIG RATIOS TO HELP US!

PRACTICE #1

PRACTICE #2

THE 3 BASIC TRIG RATIOS

•

• “SOHCAHTOA” CAN HELP YOU REMEMBER!

CALCULATOR TIPS

• MAKE SURE YOUR CALCULATOR IS IN DEGREE MODE!

• USE THE SIN, COS, AND TAN BUTTONS OF YOUR CALCULATOR TO FIND A TRIG RATIO.

• PRESS 2ND AND THE SAME BUTTONS TO FIND AN ANGLE THAT HAS THE GIVEN TRIG RATIO (INVERSE TRIG FUNCTIONS)

PRACTICE PROBLEM #1(FINDING A MISSING ANGLE)

WHICH TRIG RATIO WILL SOLVE THE PROBLEM?

PRACTICE PROBLEM #2(FINDING A MISSING ANGLE)

WHICH TRIG RATIO WILL SOLVE THE PROBLEM?

PRACTICE PROBLEM #3(FINDING A MISSING SIDE)

WHICH TRIG RATIO WILL SOLVE THE PROBLEM?

PRACTICE PROBLEM #4(FINDING A MISSING SIDE)

WHICH TRIG RATIO WILL SOLVE THE PROBLEM?