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Published byShonda Hill Modified over 7 years ago

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Trigonometry can be used for two things: 1.Using 1 side and 1 angle to work out another side, or 2.Using 2 sides to work out an angle.

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To work out things using trigonometry we use three new buttons on the calculator labelled. SinCosTan Each of these buttons has a rule you can remember by using the word: SOH-CAH-TOA

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In this word each letter stands for a word. Buttons on your calculatorSides of a Triangle S = Sin A = Adjacent C = Cos O = Opposite T = Tan H = Hypotenuse

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The Hypotenuse is the longest side. It is the one not touching the right angle. Hypotenuse

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The Opposite is the side far away from the angle you are given. 60 o Opposite 30 o

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57 o Opposite 33 o

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The Adjacent is the side next to the angle you are given. 60 o Adjacent 30 o

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49 o Adjacent 41 o

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Sin (full name sine) has the rule SOH. O H Sin θ Theta means an angle.

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Cos (full name cosine) has the rule CAH. A H Cos θ

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Tan (full name tangent) has the rule TOA. O A Tan θ

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1. Label the sides of the triangle. 2. Figure out which type of side you are looking for and which sides you have. 3. Write down the formula from SOH-CAH-TOA. 4. Put in the numbers. 5. Calculate. 6. If you are trying to find an angle you need to press: Shift Sin = Shift Cos = Shift Tan = or

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We are looking for the Opposite. We have the Hypotenuse. We need to use SOH because it has O and H. O = Sin θ × H y = Sin 30 × 24 y = 12 Opposite 30 o Adjacent Hypotenuse 24 y

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We are looking for the Opposite. We have the Hypotenuse. We need to use SOH because it has O and H. O = Sin θ × H y = Sin 48 × 15 y = 11.1 Opposite 48 o Adjacent Hypotenuse 15 y

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We are looking for the Adjacent. We have the Hypotenuse. We need to use CAH because it has A and H. A = Cos θ × H y = Cos 28 × 20 y = 17.7 Opposite 28 o Adjacent Hypotenuse 20 y

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We are looking for the Opposite. We have the Adjacent. We need to use TOA because it has O and A. A = Tan θ × A y = Tan 40 × 23 y = 19.3 Opposite 40 o Adjacent Hypotenuse 23 y

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We are looking for the Hypotenuse. We have the Opposite. We need to use SOH because it has O and H. H = O ÷ Sin θ y = 6.0 ÷ Sin 40 y = 9.3 Opposite 40 o Adjacent Hypotenuse 6.0 y

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We are looking for the Adjacent. We have the Hypotenuse. We need to use CAH because it has A and H. A = Cos θ × H y = Cos 50 × 100 y = 64.3 Opposite 50 o Adjacent Hypotenuse 100 y

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We are looking for the Opposite. We have the Adjacent. We need to use TOA because it has O and A. O = Tan θ × A y = Tan 32 × 1.4 y = 0.9 Opposite 32 o Adjacent Hypotenuse 1.4 y

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We are looking for the Hypotenuse. We have the Adjacent. We need to use CAH because it has A and H. H = A ÷ Cos θ y = 32.5 ÷ Cos 40 y = 42.4 Opposite 40 o Adjacent Hypotenuse 32.5 y

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We are looking for the Adjacent. We have the Opposite. We need to use TOA because it has O and A. A = O ÷ Tan θ y = 3.2 ÷ Tan 40 y = 3.8 Opposite 40 o Adjacent Hypotenuse 3.2 y

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We are looking for an angle. We have the Adjacent and the Opposite. We need to use TOA because it has O and A. Tan θ = O ÷ A Tan θ = 4 ÷ 2.2 Tan θ = 1.82 Opposite θ Adjacent Hypotenuse 2.2 4 ShiftTan = θ = 61 o

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We are looking for an angle. We have the Adjacent and the Hypotenuse. We need to use CAH because it has A and H. Cos θ = A ÷ H Cos θ = 4 ÷ 7 Cos θ = 0.57 Opposite θ Adjacent Hypotenuse 7 4 Shift Cos = θ = 55 o

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We are looking for an angle. We have the Hypotenuse and the Opposite. We need to use SOH because it has O and H. Sin θ = O ÷ H Sin θ = 8 ÷ 10 Sin θ = 0.8 Opposite θ Adjacent Hypotenuse 10 8 Shift Sin = θ = 53 o

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We are looking for an angle. We have the Hypotenuse and the Adjacent. We need to use CAH because it has A and H. Cos θ = A ÷ H Cos θ = 5 ÷ 10 Cos θ = 0.5 Opposite θ Adjacent Hypotenuse 10 5 Shift Cos = θ = 60 o

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