Trigonometry

Sin, cos, tan. Links: maths is fun

19 flashcards · Mathematics · by lakesare

  1. What's sin, cos and tan?

  2. How would you manually construct a sine graph?

    1. draw lines at 15° 2. and for each angle calculate sin θ = opposite/hypotenuse 3. x-axis is an angle (e.g. 15°), and y-axis is a sine at that angle Links: tutorial on how to construct a sine graph using a protractor

  3. Find the depth.

    sin 39° = d/30m (sine value is dimensionless, so d must also be in meters) d = 30m * sin 39° = 18.88.

  4. State law of sines.

  5. Prove law of sines.

  6. State law of cosines.

  7. How does law of cosines relate to the Pythagorean theorem?

    The law of cosines generalizes the Pythagorean theorem. If C = Pi/2, then cos C = 0, and c2 = a2 + b2. The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles

  8. Prove law of cosines.

  9. Find sin(-Pi/2).

    -1

  10. Find cos(2Pi).

    1

  11. Find tan(Pi/2).

    It's not defined! tan(Pi/2) = 1/0, and we can't divide by 0.

  12. Find tan(0).

    tan(0) = 0/1 = 0

  13. What does periodicity of sin, cos and tan imply?

    cos(A + 2Pi) = cos(A) sin(A + 2Pi) = sin(A) tan(A + Pi) = tan(A)

  14. Find cos(-x) sin(-x)

    cos(-x) = cos(x) sin(-x) = -sin(x)

  15. How does one arrive at formula?

    Just apply Pythagoras theorem to the unit circle!

  17. When working with right triangles, sine, cosine, and other trigonometric functions only make sense for angle measures more than zero and less than π/2.

    However, when defined with the unit circle, these functions produce meaningful values for any real-valued angle measure – even those greater than 2π.

  18. Name 2 ways to define a sine.

    1. Right angle (only makes sense for angle measures more than zero and less than π/2) 2. Unit circle The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse).More generally, the definition of sine (and other trigonometric functions) can be extended to any real value in terms of the length of a certain line segment in a…

  19. What's the idea behind Fourier series?

    The subject of Fourier series investigates the idea that an 'arbitrary' periodic function is a sum of trigonometric functions with matching periods.