Find sin theta if tan theta =squareroot5/2 and falls in Quadrant 3

Question

1.-squareroot5/3

2.2squareroot5/5

3.-2/3

4.squareroot5/3

Answer 1

The mnemonic device "ALL STUDENTS TAKE CALCULUS"

 helps you remember where the trig functions are positive.

 

In quadrant 3, the tangent is positive and the sine is negative.

Both x and y are negative.

 

The mnemonic device "SOH-CAH-TOA" or "Orange Horses are happy over apples"

helps you remember the formulas for the trig functions.

 

tangent = opposite/adjacent

 

so the leg that lies on the x-axis is -2 and the other leg must be -square root 5

 

Picture looks like this:

 

 

 

 

                                                -2    

                           __________________________

                          |

- square root 5    |

                          |

 

 

By pythagorean theorem, the hypotneuse is 3

 

So the sine is opposite/hypotneuse = -square root(5)/3

 

 

 

 

Answer 2

In Quadrant 3, sine is negative.  Thus, choices 2 and 4 are eliminated.

 

Further, tangent = opposite/adjacent.  And since sine = opposite/hypotenuse, the only answer it can be is the one where it has square root 5, which is choice 1.