# 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.

## Presentation on theme: "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."— Presentation transcript:

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.

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

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

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

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

57 o Opposite 33 o

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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