What formula do I use??

Question

Tan A = -2/3, 90 degrees < A < 180 degrees. What fomula do I use to find the exact value of the remaining trigonometirc function?

Answer 1

90 degrees < A < 180 degrees means that the angle is in the 2nd quadrant, where cos is negative and sin is positive.

Since tangent is opposite over adjacent, the hypotenuse would be:

(-2)^2 + (3)^2 = 4 + 9 = 13 = c^2

So the hypotenuse is sqrt(13).

From that, you should be able to see that:

sinA = 2/sqrt(13) = 2sqrt(13)/13
cosA = -3/sqrt(13) = -3sqrt(13)/13

And the rest are just reciprocals.

Answer 2

this is in the 2nd quadrant

sin^2+cos^2=1
tan^2+1=1/cos^2
cos^2=1/(tan^2+1)
cos^2 A=1/(4/9+1)=1/13/9)=9/13
cos A=3/√13=3*√13 /13
since this is in the 2nd quatrant, cos<0
cos A=-3√13 / 13

1+1/tan^2=1/sin^2
sin^2=1/(1+1/tan^2)
sin^2 A=1/(1+1/(4/9))=1/(1+9/4)=1/(13/4)=4/13

sin^ A=2/√13=2√13 / 13
cos A=-3√13 / 13

Answer 3

You have to graph a triangle in quadrant II. Tan=sin/cos, and sin=y and cos=x. so go up 3 units from the origin. then start over at the origin and go left 2 units. from your point (-2/3), make the line down to the x-axis, then start back over from (-2/3) and go to the origin. The diagonal line is your hypotenuse (sp.) Now you find the remaining trig functions. Your angle (theta) is the angle in the vertex closest to the origin. Using this angle, sin=opposite side/hypotenuse; cos=adjacent side/hypotenuse; and for csc, sec, and cot, your just flip sin, cos, and tan.

Answer 4

Pythagoras's theorem.