Hi there,
I'm wondering if anyone can help, I am currently revising and came across this example in one the books that I have. I'm wondering if someone can explain/show me how this is done.
This is a 2 part question.
Q) Write down th value of Cos30 deg, giving the answer in exact value?
A) sqaure root 3 / 2
= 1.73 / 2
= 0.87Am I doing this correctly?
Second part of the question
Q) Which other angle, Xdeg, in the range 0deg ≤ Xdeg ≤ 360deg has the same value for Cos X deg?
A) none, as confused.
Thanks in advance
2 Answers
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So for your circular functions, sin, cos, and tan they can be defined on the unit circle, or it'd be more accurate to say that they are "defined" by the unit circle
The unit circle has the equation x^2 + y^2 = 1
In more general terms, it has a radius of one and it's origin (centre) lies on the co-ordinates 0,0
A good representation can be found here:
http://en.wikipedia.org/wiki/Unit_circle
Now on your unit circle, the cos values represent your "x-axis" values and sin represents "y-axis" values. And tan = sin/cos
If you take the first quadrant of the unit circle, (the quarter in the positive x and y axis... top right)
and draw a triangle at 30 degrees you will notice that the vertex of the triangle touches the edge of the circle, the co-ordinates of this point are represented by (cos 30, sin 30)
It's a bit hard to explain here but if you look at http://www.mathsisfun.com/geometry/unit-circle.htm...
you'll see that cos 30 = root (3) / 2 and sin 30 = 1/2
also, you'll see the 45 degree triangle and the 60 degree one which will also give you are values... these values are known as your "exact values" the website provides you with a table, and it's pretty easily committed to memory.
Now with regards to the other three quadrants, as you know that cos is the x-coordinate and sin is the y-coordinate and tan is sin/cos, you find that sin is positive in the 2nd, tan is positive in the 3rd, cos is positive in the 4th and they're all positive in the third.
A good way to remember it is to draw a circle, divide into four and label each one A S T C, i.e. all positive, sin positive etc. a good example is here:
http://www.regentsprep.org/Regents/math/algtrig/AT... (near the end)
so the answers to your question:
cos 30 = root (3) / 2 --- this is considered an exact value and it is expressed so that is can't simplified any further, a decimal answer like yours is an "estimation/ approximation" answer and is therefore incorrect
part two, and cos is positive in the fourth quadrant: therefore the angle is 270 + 30 = 300
If asking for sin, then 90 + x, tan, then 180 + x
Hope that helps!
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