(Solved) How do you find the exact value of the six trigonometric functions of ? when your given a point?

nvaldivi2

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11 years ago

How do you find the exact value of the six trigonometric functions of ? when your given a point?

How do you find the exact value of the six trigonometric functions of ? when your given a point?

Example

You're given
(-4,-6)

and you need to find the

tan = sec = cos = cot = sin = csc =

How do you figure that out?

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mikael

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11 years ago

1.) Get out a piece of graph paper and graph this point. You wont "see" this unless you do.

2.) y= -6 and x= -4....Now use Pythagorean Identity to solve for r..

3.) 36 + 16 =r^2.....r=2sqrt(13)

4.) We know x, y, and r...We ALSO know that this is a QUADRANT 3 angle

5.) Watch your SIGNS!

sin =y/r
cos=x/r
tan=y/x
cot=x/y
sec=r/x
csc=r/x

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ilikescience

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11 years ago

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Mickymouse

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11 years ago

I'm assuming there is a line from the origin (0,0) to this point and you need to measure the anticlockwise angle from the positive x-axis. This is standard procedure.

So you find out the angle between this line and the negative x-axis using trigonometry (you have the adjacent and opposite angles, so use tan to find it) then add 180degrees to find ? and do your thing!

-----

If you can't sue a calculator, work out the 6 trig values on the line (tan = opp/adj = 4/6 = 2/3 for example) and note that in this quadrant, Tan values are positive but cos and sin values are negative.

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mikael

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11 years ago

The tangent will be -4/-6 = 2/3. Use the arctan function to find theta [33.6 degrees or .588 radians] , then do the other trig functions on theta. Remember that you are in the third quadrant, so sin and cos will be negative.

There are some identities so you can find the other functions by algebraic manipulation, but they are a pain in the tail.

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