Concept 4 Problems Solving Trig Functions

Level 1

In this level, we simply take the trig function we have and find out how we get the given value through the unit circle. since we know that tan is x/y, we know that we can get the ratio rad3/3 with 1/2/rad3/3. the given points are found in the 60 degree, and also in 240 degree, since it is a positive function.








Level 2

The second level, we deal with simple problem solving. we must get the sin (x) by itself. In this case, we are getting no solution since sin must be -1<x<1.












Level 3
In this level, we deal with more complicated solving. we must get a common trig function, and since we know from the ratio identity, csc=1/sin, and cot=cos/sin. there is a common denominator, so we combine the equation. next, we must multiply sin to both sides. since we are now stuck, we must square both sides. we know that sin^2(x) is 1-cos^2. finally, we take what is given, and combine like terms, having a zero on the right side. we take out the common factor which is 2cos. then, we solve for both terms.
Don't forget that there may be extraneous solutions!


Level 4

In this level of problem, we are looking for half/double angles. We need to replace the function with "m", then solve for m. when we do, we take what is solve, 360 and 180, and equal it to x/4. put it as "x" and get the final angles.