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: 𝑎 2 + 𝑏 2 = 𝑐 2 …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 𝑎 2 + 𝑏 2 = 𝑐 2 11 2 + 11 2 = 𝑐 2 121+121= 𝑐 2 242= 𝑐 2 𝑐= 242 ≈15.56 𝑘𝑚

Practice #2 𝑎 2 + 𝑏 2 = 𝑐 2 𝑥 2 + 4.9 2 = 6.2 2 𝑥 2 +24.01=38.44 𝒙 𝟐 =𝟑𝟖.𝟒𝟒−𝟐𝟒.𝟎𝟏 𝑥 2 =14.43 𝑥= 14.43 ≈3.80 𝑚

The 3 Basic Trig Ratios “SOHCAHTOA” can help you remember! sin 𝜃 = 𝑂𝑃𝑃 𝐻𝑌𝑃 = 𝑂 𝐻 cos 𝜃 = 𝐴𝐷𝐽 𝐻𝑌𝑃 = 𝐴 𝐻 tan 𝜃 = 𝑂𝑃𝑃 𝐴𝐷𝐽 = 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 = 14 20 =0.7 𝜃= sin −1 (0.7)≈44.4°

Practice Problem #2 (Finding a Missing Angle) Which trig ratio will solve the problem? CO𝑆 𝜃 = 𝐴𝐷𝐽 𝐻𝑌𝑃 COS 𝜃 = 12 13 𝜃= COS −1 ( 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