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

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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 0.642787… 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. 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 Try each of these on your calculator: sin 55° sin 10° sin 87° Sine Function

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Try each of these on your calculator: sin 55° = 0.819 sin 10° = 0.174 sin 87° = 0.999 Sine Function

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Inverse Sine Function Using sin -1 (inverse sin): If 0.7315 = sin θ then sin -1 (0.7315) = θ Solve for θ if sin θ = 0.2419 Inverse Sine Function

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

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Use your calculator to determine cos 50° First, type-in 50… …then press the cos key. You should get an answer of 0.642787... 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. Cosine Function

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Try these on your calculator: cos 25° cos 0° cos 90° cos 45° Cosine Function

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Try these on your calculator: cos 25° = 0.906 cos 0° = 1 cos 90° = 0 cos 45° = 0.707 Cosine Function

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Using cos -1 (inverse cosine): If 0.9272 = cos θ then cos -1 (0.9272) = θ Solve for θ if cos θ = 0.5150 Inverse Cosine Function

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

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Use your calculator to determine tan 40° First, type-in 40… …then press the tan key. You should get an answer of 0.839... 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 Try these on your calculator: tan 5° tan 30° tan 80° tan 85°

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Tangent Function Try these on your calculator: tan 5° = 0.087 tan 30° = 0.577 tan 80° = 5.671 tan 85° = 11.430

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

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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 Review

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The sin function: sin A = A opposite hypotenuse

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

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The tangent function. tan A = A adjacent opposite Review

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Most Common Application: x y r θ

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

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Solve for θ: 0.7987 = sin θ 0.9272 = cos θ 2.145 = tan θ Review

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What if its not a right triangle? - Use the Law of Cosines: The Law of Cosines In any triangle ABC, with sides a, b, and c,

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What if its 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. R 2 = A 2 + B 2 – 2AB cosθ θ

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