Trignometry vbei
- 1. Vidya Bharti Educational Institutions
- 2. Trigonometry Basics Right Triangle Trigonometry
- 4. Sine FunctionSine 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.
- 5. Sine functionSine function Given a right triangle, and reference angle A: sin A = hypotenuse opposite A opposite hypotenuse The sin function specifies these two sides of the triangle, and they must be arranged as shown.
- 6. Sine FunctionSine 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,Note: If this did not work on your calculator, try pressing thetry pressing the sinsin key first, then type-in 40.key first, then type-in 40. Press the = key to get the answer.Press the = key to get the answer.
- 7. Sine Function Try each of these on your calculator: sin 55° sin 10° sin 87° Sine FunctionSine Function
- 8. Sine Function Try each of these on your calculator: sin 55° = 0.819 sin 10° = 0.174 sin 87° = 0.999 Sine FunctionSine Function
- 9. Inverse Sine FunctionInverse 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 FunctionInverse Sine Function
- 10. Cosine function The next trig function you need to know is the cosine function (cos): cos A = hypotenuse adjacent A adjacent hypotenuse Cosine FunctionCosine Function
- 11. 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. Cosine FunctionCosine Function
- 12. Cosine Function Try these on your calculator: cos 25° cos 0° cos 90° cos 45° Cosine FunctionCosine Function
- 13. Cosine Function Try these on your calculator: cos 25° = 0.906 cos 0° = 1 cos 90° = 0 cos 45° = 0.707 Cosine FunctionCosine Function
- 14. 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 FunctionInverse Cosine Function
- 15. Tangent function The last trig function you need to know is the tangent function (tan): tan A = adjacent opposite A adjacent opposite Tangent FunctionTangent Function
- 16. Tangent FunctionTangent 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.
- 17. Tangent Function Try these on your calculator: tan 5° tan 30° tan 80° tan 85° Tangent FunctionTangent Function
- 18. Tangent Function Try these on your calculator: tan 5° = 0.087 tan 30° = 0.577 tan 80° = 5.671 tan 85° = 11.430 Tangent FunctionTangent Function
- 19. Using tan-1 (inverse tangent): If 0.5543 = tan θ then tan-1 (0.5543) = θ Solve for θ if tan θ = 28.64 Inverse Tangent FunctionInverse Tangent Function
- 20. 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 adj opp A hyp adj A hyp opp A = = = tan cos sin Review
- 21. Review The sin function: sin A = hypotenuse opposite A opposite hypotenuse
- 22. Review The cosine function. cos A = hypotenuse adjacent A adjacent hypotenuse Review
- 23. Review The tangent function. tan A = adjacent opposite A adjacent opposite Review
- 24. Most Common Application: 2 2 1 cos sin tan r x y x r y r y x θ θ θ − = + = = = ÷ x y r θ
- 25. Review Solve for x: x = sin 30° x = cos 45° x = tan 20° Review
- 26. Review Solve for θ: 0.7987 = sin θ 0.9272 = cos θ 2.145 = tan θ Review
- 27. 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, .cos2 cos2 cos2 222 222 222 Cabbac Baccab Abccba −+= −+= −+=
- 28. 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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