Basics of Trigonometry Click triangle to continue

What is Trigonometry? Right Angled Triangles Sine Cosine and Tangent Pythagorean Theorem What is Trigonometry? Right Angled Triangles Sine Cosine and Tangent Pythagorean Theorem CLICK HERE FOR QUIZ!

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/ cos(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: a 2 + b 2 = c 2 Remember that “c” is the hypotenuse Can you find the answer to “c”?

How to Solve for “C” (Steps) Step 1: write out equation a 2 + b 2 = c 2 Step 2: plug in numbers = c 2 Step 3: square the numbers = c 2 Step 4: add like terms 169 = c 2 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

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