UnbelievableDreams
  • UnbelievableDreams
Confusing math question
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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UnbelievableDreams
  • UnbelievableDreams
Find the exact value of s in the given circular function value. Do not use a calculator. [0, pi/2]; sin s = sqrt3/ 2 I will be offline for an hour because my grandfather needs me. Can you please show me how to do this? Thank you.
anonymous
  • anonymous
Use the unit cirycle. The x-coordinates give cosines and the y-coordinates give sines. The part in brackets tells you that you're looking for angles between 0 and π/2 inclusive. That's the first quadrant. So you're looking for the angle in radians that has a y-coordinate of \(\frac{ \sqrt{3} }{ 2 }\). |dw:1437169225134:dw|
UnbelievableDreams
  • UnbelievableDreams
I got it. But what about tan? I always get wrong answer.

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anonymous
  • anonymous
tan Θ = y/x, so if you wanted to find \(\tan \frac{\pi}{3}\) divide \(\frac{ \sqrt{3} }{ 2 }\) by ½. \[\tan \frac{ \pi }{ 3 }=\frac{ \sqrt{3} }{ 2 }\div \frac{ 1 }{ 2 }=\frac{ \sqrt{3} }{ 2 }\times \frac{ 2 }{ 1 }=\sqrt3\]
UnbelievableDreams
  • UnbelievableDreams
I am still confused. :(
UnbelievableDreams
  • UnbelievableDreams
I wonder how you get sqrt3 / 2 and 1/2
anonymous
  • anonymous
They come from the circle. I just used π/3 as an example. At π/3, the (x,y) point is \((\frac{ 1 }{ 2 },\frac{ \sqrt3 }{ 2 })\). And then to find the tangent, divide the y coordinate by the x coordinate.
UnbelievableDreams
  • UnbelievableDreams
I see. Like for example, tan s (sqrt 3) I can't find sqrt 3 so it is sqrt/3
anonymous
  • anonymous
tan ratios are not on most circles explicitly, so you have a few options. IMO, the quickest is to memorize the tan values for the 1st quadrant and then relate them to the others. tan 30° = tan π/6 = 1/√3 = (√3)/3 tan 45° = tan π/4 = 1 tan 60° = tan π/3 = √3 You can also derive it with a right triangle. If tan Θ is 1 or -1, the triangle is 45-45-90 and is an odd multiple of π/4. If tan is ±√3 or ±(√3)/3 then it's a 30-60-90 triangle and you can use the values to figure out if the angle is 30° or 60°. |dw:1437186512607:dw|
UsukiDoll
  • UsukiDoll
[0, pi/2] means that from 0 to 90 degrees we are in the first quadrant
UsukiDoll
  • UsukiDoll
pi/2 x 180/pi = 180/2=90 degrees we use 180/pi to convert from radians to degrees we use pi/180 to convert from degrees to radians
UsukiDoll
  • UsukiDoll
memorizing the 30,45,60 degree triangles work too.
UnbelievableDreams
  • UnbelievableDreams
I see.
UsukiDoll
  • UsukiDoll
|dw:1437187176412:dw|

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