Easy: Cos 2π/3= -1/2
*find 2π/3
*remember cos is the x value
*the x value is -1/2
Medium: Tan of π=0
*find π
*it is (-1,0)
*remember tan is y/x
*that would make it 0/-1
*whenever you have 0/anything the answer is always 0
Hard: Cot of π/3=√3/3
*remember that Cot is x/y
*find π/3 on the unit circle
*you see (1/2, √3/2)
*so you will have 1/2/ √3/2
*once again use the copy change flip rule
*copy the 1/2 change the sign to multiplication and flip √3/2 to 2/√3
*so you have 1/2 X 2/√3
*the 2s cancel so you are left with 1/√3
*you cant have a square root in the denominator so multiply the top and bottom by √3 to get rid of it
*you are left with √3/3
Real World:You are give Sin=-3/4 and Tan is less than 0. Find X
*First use the All Students Take Calculus rule to find which quadrant you are in
*This rule is that All=quadrant 1, Students=quadrant 2, Take=quadrant 3, and Calculus=quadrant 4
* All means that they are all positive, Students means Sin is positive, Take means Tan is positive, and Calculus means Cos is positive
* since tan is less than 0 that means its either in quadrant 2 or 4
*since sin is negative that means it must be in quadrant 4
*use the Pythagorean theorem to find x
*Sin is y/r
*so you set up the equation as -3 squared + x squared=4 squared
*that gives you 9 + x squared=16
*subtract 9 from both sides
*this leaves you x squared=7
*square root both sides
*this leaves you x=√7
*find 2π/3
*remember cos is the x value
*the x value is -1/2
Medium: Tan of π=0
*find π
*it is (-1,0)
*remember tan is y/x
*that would make it 0/-1
*whenever you have 0/anything the answer is always 0
Hard: Cot of π/3=√3/3
*remember that Cot is x/y
*find π/3 on the unit circle
*you see (1/2, √3/2)
*so you will have 1/2/ √3/2
*once again use the copy change flip rule
*copy the 1/2 change the sign to multiplication and flip √3/2 to 2/√3
*so you have 1/2 X 2/√3
*the 2s cancel so you are left with 1/√3
*you cant have a square root in the denominator so multiply the top and bottom by √3 to get rid of it
*you are left with √3/3
Real World:You are give Sin=-3/4 and Tan is less than 0. Find X
*First use the All Students Take Calculus rule to find which quadrant you are in
*This rule is that All=quadrant 1, Students=quadrant 2, Take=quadrant 3, and Calculus=quadrant 4
* All means that they are all positive, Students means Sin is positive, Take means Tan is positive, and Calculus means Cos is positive
* since tan is less than 0 that means its either in quadrant 2 or 4
*since sin is negative that means it must be in quadrant 4
*use the Pythagorean theorem to find x
*Sin is y/r
*so you set up the equation as -3 squared + x squared=4 squared
*that gives you 9 + x squared=16
*subtract 9 from both sides
*this leaves you x squared=7
*square root both sides
*this leaves you x=√7
