The coordinates of the point P(−2, 7) on a terminal arm of an angle θ, in standard position, are given, where 0^0 ≤ θ ≤ 360^0

Question

a) Determine the exact values of sinθ, secθ, and cotθ.

b) Determine angle θθ.

c) What is the measure of the first negative coterminal angle?

Answer 1

P(-2,7) is in Quadrant II where only sinT & cscT>0

secants, cosines, tangents, cotangents all <0

constuct a right triangle with vertices (0,0), (-2,7), (-2,0)

h=hypotenuse =sqr(7^2+2^2)=sqr53

a = adjacent side =-2

o = oppsite side =7

sinT= o/h= 7/sqr53

secT=h/a =-sqr53/2

cotT= a/o =-2/7

to find T, use a calculator with inverse trig functions

T= cos^-1(-2/sqr53)= about 180- 74.055= 105.945 degrees

1st negative coterminal angle is 105.945 -360= - 254.055 degrees

Answer 2

You can sketch out an x-y coordinate plane, mark (-2,7) and draw a line from the origin (0,0) to that point. That's the terminal arm of the angle.

a) You can use SOH CAH TOA where the x = -2 is the A, y = 7 is the O, and sqrt((-2)^2 + 7^2) = sqrt(53) is the H. The "exact value" means you should leave the answer with the sqrt symbol and as a fraction.

b) You need to use the calculator to get the arcsin of whatever you got for sin Θ. That's the angle. BTW, when the problem says 0 ≤ Θ ≤ 360, that means the teacher wants the answer in degrees.

c) To get the first negative coterminal angle, just subtract 360 from the angle you got above.

Answer 3