Download Trigonometry

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:
𝑎2 + 𝑏2 = 𝑐 2
…WHERE A AND B ARE THE LEGS AND C IS THE
HYPOTENUSE.
PRACTICE #1
𝑎2 +𝑏2 = 𝑐 2
112 + 112 = 𝑐 2
121 + 121 = 𝑐 2
242 = 𝑐 2
𝑐 = 242 ≈ 15.56 𝑘𝑚
PRACTICE #2
𝑎2 + 𝑏2 = 𝑐 2
𝑥 2 + 4.92 = 6.22
𝑥 2 + 24.01 = 38.44
𝒙𝟐 = 𝟑𝟖. 𝟒𝟒 − 𝟐𝟒. 𝟎𝟏
𝑥 2 = 14.43
𝑥 = 14.43 ≈ 3.80 𝑚
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!
THE 3 BASIC TRIG RATIOS
• SIN 𝜃 =
𝑂𝑃𝑃
𝐻𝑌𝑃
• COS 𝜃 =
𝐴𝐷𝐽
𝐻𝑌𝑃
• TAN 𝜃 =
𝑂𝑃𝑃
𝐴𝐷𝐽
=
𝑂
𝐻
=
𝐴
𝐻
=
𝑂
𝐴
• “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?
SIN 𝜃 =
𝑂𝑃𝑃
𝐻𝑌𝑃
SIN 𝜃 =
𝜃=
14
−1
SIN
20
14
20
≈ 44.4°
PRACTICE PROBLEM #2
(FINDING A MISSING ANGLE)
WHICH TRIG RATIO WILL SOLVE THE PROBLEM?
CO𝑆 𝜃 =
𝐴𝐷𝐽
𝐻𝑌𝑃
COS 𝜃 =
𝜃=
12
−1
COS
13
12
13
≈ 22.6°
PRACTICE PROBLEM #3
(FINDING A MISSING SIDE)
WHICH TRIG RATIO WILL SOLVE THE PROBLEM?
TAN 43° =
𝑂𝑃𝑃
𝐴𝐷𝐽
TAN 43° =
𝑎
11
𝑎 = 11 ∗ TAN 43° ≈ 10.3
PRACTICE PROBLEM #4
(FINDING A MISSING SIDE)
WHICH TRIG RATIO WILL SOLVE THE PROBLEM?
COS 50° =
𝐴𝐷𝐽
𝐻𝑌𝑃
COS 50° =
17
𝑥
𝑥 ∗ COS 50° = 17
𝑥=
17
COS 50°
≈ 26.4