Basics of Trigonometry
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What is Trigonometry?
Right Angled Triangles
Sine Cosine and Tangent
Pythagorean Theorem
What is Trigonometry?
• Trigonometry (from Greek trigonon "triangle" + metron "measure")
• Trig is all about triangles!
• The three sides of the triangle are labeled
• Hypotenuse
• Adjacent
• Opposite
Right Angled Triangles
• We can find any angle of a right triangle as long as we have the
lengths of 2 sides.
• We can find the length of any side of a right triangle as long as we
have at least one angle and side.
• If given one angle, add 90 and subtract sum from 180
to find the missing angle of the triangle
(HELPFUL HINTS)
• *SOH CAH TOA can only be used for right triangles*
• *The hypotenuse is ALWAYS across from the right angle*
Sine, Cosine, and Tangent
• We use these three trig functions to find the angles and sides of right
triangles.
• For short we use the term SOH-CAH-TOA
• SOH: Sin = opposite/hypotenuse
• CAH: Cos = adjacent/hypotenuse
• TOA: Tan = opposite/adjacent
• Lets look at some examples
A.) Example of a triangle with a length and
angle
• Step 1: The two sides we are using are Adjacent (h) and Hypotenuse
(1000).
• Step 2: SOH-CAH-TOA tells us to use Cosine.
• Step 3: Put our values into the Cosine equation: cos 60° = Adj/ Hyp
cos 60° = h / 1000
• Step 4 Solve:
Solving The Problem
• Find the height of the plane
• (h = height)
• Cos 60° = h/1000 so by using basic algebra, we know to plug
1000cos(60) into the calculator to find the height of the plane!
• Cos 60° = h/1000
• 1000cos(60°) = h
• Height = 500
B.) Example of a triangle with 2 Side Lengths
• Step 1: The two sides we know are Opposite (300) and Adjacent(400).
• Step 2: SOH-CAH-TOA tells us we must use Tangent.
• Step 3: Calculate Opposite/Adjacent = 300/400 = 0.75
• Step 4: Find the angle from your calculator using tan-1
• We use the inverse of Sine, Cosine, and Tangent to find missing angles
Solving The Problem
• Find the angle of elevation
• You can solve this problem two different ways
• Tan-1 (300/400) = answer
• OR
• 300/400 = 0.75 so Tan-1 (0.75) = answer
• The answer is 36.87°
Pythagorean Theorem
• When we are trying to find just the sides of the triangle, we use the
Pythagorean theorem.
• This equation only works for right triangles!
• Equation: a2 + b2 = c2
• Remember that “c” is the hypotenuse
• Can you find the answer to “c”?
How to Solve for “C” (Steps)
• Step 1: write out equation a2 + b2 = c2
• Step 2: plug in numbers 52 + 122 = c2
• Step 3: square the numbers 25 + 144 = c2
• Step 4: add like terms 169 = c2
• Step 5: take the square root c = √169
• Step 6: final answer c = 13
QUIZ!
• What two sides would we use for a problem dealing with Cosine?
• A.) opposite/hypotenuse
• B.) opposite/adjacent
• C.) adjacent/hypotenuse
A.) opposite/hypotenuse
Sorry! Try again
• Opposite/Hypotenuse is used for Sine
• Remember *SOH-CAH-TOA*
B.) Opposite/Adjacent
Sorry! Try again
• Opposite/Adjacent is used for Tangent
• Remember *SOH-CAH-TOA*
C.) Adjacent/Hypotenuse
Great Job! You got it!
• Adjacent/Hypotenuse is used for Cosine
You have completed the lesson!
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