read the problem below

Question

Given an angle theta in standard position fill in the blanks within the diagram below to indicate if the trigonometric value of theta would be positive (+) or negative (-)       

       l                             lll

 sin(theta) is                 sin(theta) is

                                  tan(theta) is
cos(theta) is                  Cos(theta) is
tan(theta)is
                                      lV

                                     sin(theta) is
                                    cos(theta) is
                                    tan(theta)is              ll

sin(theta) is 

cos(theta) is 

tan(theta)is 

Answer 1

In quadrants I through IV, respectively, sine is + + - -

cosine is + - - +

tangent is + - + -

 

This is clearly understandable and easy to visualize if you work with the UNIT CIRCLE and a full (0 to 360 deg.) angle's REFERENCE TRIANGLE, in which case the vertical coordinate is actually the sine of the original angle and the horizontal component is actually the cosine of the original angle (and the hypotenuse is 1, of course--a physical example of the Pythagorean identity).