Re: Values for sec, tan, cot cos
Ok im instructed to find the value of the following, without using decimals and without a calculator.
cos 330 degrees
so i am tempted to just answer the question by calling it 11pi/6
I know thats too easy....so what are they looking for here?
All these trig functions are ratios of one side of a triangle to another. You know that 330 is in the 4th quadrant, so start by drawing a triangle in the 4th quadrant. The hypotenuse of the triangle is along the 330 degree line. From some point on the 330 degree line, draw a line perpendicular to the x axis (never to the y axis). That completes our triangle.
So, what kind of triangle is it? What are the angles? Obviously, it’s a 30-60-90 triangle.
We know the ratio of the sides for this triangle (or at least we’re expected to know). Label the short side (the one opposite the 30 degree angle) as “x”. The hypotenuse is twice as long as the short side, so label it “2x”. The other leg (the one along the x axis) is x(3)^.5 (that’s x times the square root of 3).
You also know that cosine of an angle is the ratio of the adjacent side to the hypotenuse, so we use that info to give our final answer.
So to summarize:
1) Figure out which quadrant you’re in.
2) Draw a triangle in that quadrant.
3) Figure out what kind of triangle it is (what the angles are).
4) Label the lengths of all the sides.
5) Find the requested ratio.
