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We know

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$\\sin0^o=0\\ \\ ,\\cos0^O=1\\ ,\\tan0^o=0\\\\\\sin30^o=\\dfrac{1}{2}\\ ,\\cos30^o=\\dfrac{\\sqrt{3}}{2} ,\\tan30^O=\\dfrac{1}{\\sqrt{3}}\\\\\\sin45^o=\\dfrac{1}{\\sqrt{2}}\\ ,\\cos45^O=\\dfrac{1}{\\sqrt{2}} ,\\tan45^O=1\\\\\\sin60^o=\\dfrac{\\sqrt{3}}{2}\\ ,\\cos60^o=\\dfrac{1}{2}\\ ,\\tan60^o=\\sqrt{3} \\\\\\sin90^o=1\\ ,\\cos90^O=0\\ ,\\tan90^o=\\text{Undefined}$.

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Supposing we have a large angle ,we have to find how many complete rotations have been covered and what is the extra angle. To get this we have to divide the angle $\\alpha$ by $360$ and get the remainder. Supposing $\\alpha=360^o\\times n+r$. where $r$ is the remainder , then $\\sin(\\alpha)=\\sin(r)$. The same applies to other ratios as well.

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Now find the values in the following questions.

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  1. $\\sin\\var{a}=\\sin\\var{amod}$
  2. \n
  3. $\\sin\\var{b}=\\sin\\var{bmod}$
  4. \n
  5. $\\sin\\var{c}=\\sin\\var{cmod}$
  6. \n
  7. $\\sin\\var{d}=\\sin\\var{dmod}$
  8. \n
  9. $\\tan\\var{d}=\\sin\\var{dmod}$
  10. \n
  11. $\\sin\\var{p}=\\sin\\var{pmod}$
  12. \n
  13. $\\cos\\var{q}=\\cos\\var{qmod}$
  14. \n
  15. $\\cos\\var{r}=\\cos\\var{rmod}$
  16. \n
  17. $\\cos\\var{s}=\\cos\\var{smod}$
  18. \n
  19. $\\cos\\var{t}=\\cos\\var{tmod}$
  20. \n
  21. $\\cos\\var{u}=\\cos\\var{umod}$
  22. \n
  23. $\\cos\\var{v}=\\cos\\var{vmod}$
  24. \n
  25. $\\tan\\var{w}=\\tan\\var{wmod}$
  26. \n
  27. $\\tan\\var{x}=\\tan\\var{xmod}$
  28. \n
  29. $\\tan\\var{y}=\\tan\\var{ymod}$
  30. \n
  31. $\\tan\\var{z}=\\tan\\var{zmod}$
  32. \n
  33. $\\tan\\var{l}=\\tan\\var{lmod}$
  34. \n
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All these have sine as equal to sin(30)=1/2

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All these have value= sin(45)

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All these have value=sin(60)

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All these have value=sin(0)=tan(0)

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All these have value=sin(90)=1

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All thest have value=cos(0)

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All these have value=cos(30)

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All thes have value=cos(45)

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\n

All these have value=cos(60)

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All these have value=cos(90)=0

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All these have value=cos(180)=-1

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All these have value=tan(30)

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All these have value=tan(45)

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All these have value=tan(60)

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All these will give value=tan(90)=undefined

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All these will give value=tan(135)=-1

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$\\sin\\var{a}^\\circ$=

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$\\cos\\var{r}^\\circ$=

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$\\tan\\var{w}^\\circ=$

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$\\sin\\var{b}^\\circ$=

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$\\cos\\var{t}^\\circ$=

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$\\tan\\var{x}^\\circ$=

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$\\tan\\var{l}^\\circ$=

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$\\cos\\var{q}^\\circ$=

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$\\tan\\var{y}^\\circ$=

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$\\cos\\var{v}^\\circ$=

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$\\sin\\var{c}^\\circ$=

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$\\cos\\var{s}^\\circ$=

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$\\sin\\var{p}^\\circ$=

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$\\sin\\var{d}^\\circ$=

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$\\cos \\var{u}^\\circ$=

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$\\tan \\var{z}^\\circ$=

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