An angle is in standard position and has terminal point P. For each, find the radius of the circle (in exact form) and the measure of the angle to the nearest tenth of a degree: a) P(5, −8) b) P(-9,7)

Question

grade 11 mixd functions

Answer 1

a) P(5,-8) has hypotenuse sqr(25+64) = sqr89 = the radius of the circle

tanA = -8/5. A is in the 2nd or 4th quadrant

A= tan^-1(-8/5) =180- 57.99= 122.01 degrees = 122.0 degrees rounded to nearest tenth

or -58 +360 = 302.0 degrees

plus 360n where n = any integer

or just more briefly

A= 122 +180n degrees where n=any integer

b) P(-9,7) has hypotenuse sqr(81+49) = sqr130 = the radius of the circle

tanB = -7/9 B is in either the 2nd or 4th quadrant

B = tan^-1(-7/9) = 37.87

B = 180-37.87 = 142.13 = 142.1 degrees rounded to nearest 10th

or

B= -37.87+360 = 322.13 = 322.1 degrees rounded to nearest 10th

plus 360n where n= any integer

or more briefly B = 142.1 plus 180n where n=any integer