## anonymous one year ago Determine all points of intersection y=cosX and y=sinX in the first quadrant

1. anonymous

o my i wish i know..sorry i don't know

2. arindameducationusc

easy

3. arindameducationusc

sin45=cos45

4. arindameducationusc

hope that works

5. anonymous

Yes I know it's 45(pi/4) but is there any math involved? I found the answer by looking at a graph...

6. arindameducationusc

in terms of triangle... well try imagining with random values in which sin and cos value merge....

7. AakashSudhakar

Well, the more accurate answer would be:$\frac{ \pi }{ 4 }+2n \pi$This is because every 2*pi you go out in the positive direction, you'll have another intersection of the cosine and sine graphs in the first quadrant. This is a property generally held true for any intersection relationships between sinusoidal functions.

8. arindameducationusc

@AakashSudhakar How will you explain why the pi/4 came? We know its pi/4.

9. UsukiDoll

maybe it's from the 45 degree angle special triangle?

10. UsukiDoll

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11. AakashSudhakar

You can do this either by simply plugging in values into the expression: $\sin \theta = \cos \theta$and seeing what works. Or, you can use the unit circle. Create a unit circle, look at the first quadrant, and see which value on the unit circle allows sin(theta) and cos(theta) to traverse the same distance. I prefer the unit circle method, it's much faster and very accurate.

12. AakashSudhakar