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Trigonometry Basics

Trigonometry Basics. Right Triangle Trigonometry. 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. Sine function. Given a right triangle, and reference angle A:.

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Trigonometry Basics

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  1. Trigonometry Basics Right Triangle Trigonometry

  2. 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.

  3. Sine function • Given a right triangle, and reference angle A: The sin function specifies these two sides of the triangle, and they must be arranged as shown. sin A = hypotenuse opposite A

  4. 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.

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

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

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

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

  9. 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 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.

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

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

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

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

  14. Tangent Function • 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.

  15. Tangent Function Tangent Function • Try these on your calculator: • tan 5° • tan 30° • tan 80° • tan 85°

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

  17. Inverse Tangent Function • Using tan-1 (inverse tangent): If 0.5543 = tanθ then tan-1 (0.5543) = θ • Solve for θ if tan θ = 28.64

  18. 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

  19. hypotenuse opposite Review • The sin function: sin A = A

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

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

  22. Most Common Application: r y θ x

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

  24. Review Review • Solve for θ: 0.7987 = sinθ 0.9272 = cosθ 2.145 = tanθ

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

  26. 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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