## UnbelievableDreams one year ago Confusing math question

1. 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.

2. 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|

3. UnbelievableDreams

I got it. But what about tan? I always get wrong answer.

4. anonymous

tan Θ = y/x, so if you wanted to find $$\tan \frac{\pi}{3}$$ divide $$\frac{ \sqrt{3} }{ 2 }$$ by ½. $\tan \frac{ \pi }{ 3 }=\frac{ \sqrt{3} }{ 2 }\div \frac{ 1 }{ 2 }=\frac{ \sqrt{3} }{ 2 }\times \frac{ 2 }{ 1 }=\sqrt3$

5. UnbelievableDreams

I am still confused. :(

6. UnbelievableDreams

I wonder how you get sqrt3 / 2 and 1/2

7. 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.

8. UnbelievableDreams

I see. Like for example, tan s (sqrt 3) I can't find sqrt 3 so it is sqrt/3

9. 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|

10. UsukiDoll

[0, pi/2] means that from 0 to 90 degrees we are in the first quadrant

11. 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

12. UsukiDoll

memorizing the 30,45,60 degree triangles work too.

13. UnbelievableDreams

I see.

14. UsukiDoll

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