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**Right Triangle Trigonometry**

Trigonometry Basics Right Triangle Trigonometry

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Sine Function When you talk about the sin of an angle, that means you are working with the opposite side, and the hypotenuse of a right triangle.

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**Sine function Given a right triangle, and reference angle A: sin A =**

The sin function specifies these two sides of the triangle, and they must be arranged as shown. sin A = hypotenuse opposite A

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**Sine Function For example to evaluate sin 40°…**

Type-in 40 on your calculator (make sure the calculator is in degree mode), then press the sin key. It should show a result of … Note: If this did not work on your calculator, try pressing the sin key first, then type-in 40. Press the = key to get the answer.

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**Sine Function Sine Function Try each of these on your calculator:**

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**Sine Function Sine Function Try each of these on your calculator:**

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**Inverse Sine Function Inverse Sine Function Using sin-1 (inverse sin):**

If = sin θ then sin-1 (0.7315) = θ Solve for θ if sin θ =

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**Cosine function Cosine Function**

The next trig function you need to know is the cosine function (cos): cos A = hypotenuse A adjacent

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**Cosine Function Cosine Function**

Use your calculator to determine cos 50° First, type-in 50… …then press the cos key. You should get an answer of Note: If this did not work on your calculator, try pressing the cos key first, then type-in 50. Press the = key to get the answer.

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**Cosine Function Cosine Function Try these on your calculator: cos 25°**

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**Cosine Function Cosine Function Try these on your calculator:**

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**Inverse Cosine Function**

Using cos-1 (inverse cosine): If = cos θ then cos-1 (0.9272) = θ Solve for θ if cos θ =

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**Tangent function Tangent Function**

The last trig function you need to know is the tangent function (tan): tan A = opposite A adjacent

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**Tangent Function Use your calculator to determine tan 40°**

First, type-in 40… …then press the tan key. You should get an answer of Note: If this did not work on your calculator, try pressing the tan key first, then type-in 40. Press the = key to get the answer.

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**Tangent Function Tangent Function Try these on your calculator: tan 5°**

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**Tangent Function Tangent Function Try these on your calculator:**

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**Inverse Tangent Function**

Using tan-1 (inverse tangent): If = tan θ then tan-1 (0.5543) = θ Solve for θ if tan θ = 28.64

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Review Review These are the only trig functions you will be using in this course. You need to memorize each one. Use the memory device: SOH CAH TOA

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Review The sin function: sin A = hypotenuse opposite A

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Review Review The cosine function. cos A = hypotenuse A adjacent

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Review Review The tangent function. tan A = opposite A adjacent

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**Most Common Application:**

r y θ x

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Review Review Solve for x: x = sin 30° x = cos 45° x = tan 20°

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Review Review Solve for θ: = sin θ = cos θ = tan θ

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**What if it’s not a right triangle? - Use the Law of Cosines:**

In any triangle ABC, with sides a, b, and c,

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**What if it’s not a right triangle?**

Law of Cosines - The square of the magnitude of the resultant vector is equal to the sum of the magnitude of the squares of the two vectors, minus two times the product of the magnitudes of the vectors, multiplied by the cosine of the angle between them. R2 = A2 + B2 – 2AB cosθ θ

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Finding a Missing Angle of a Right Triangle. EXAMPLE #1 First: figure out what trig ratio to use in regards to the angle. Opposite and Adjacent O,A.

Finding a Missing Angle of a Right Triangle. EXAMPLE #1 First: figure out what trig ratio to use in regards to the angle. Opposite and Adjacent O,A.

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