If tan x=5/2 for pi less than or equal to x less than or equal to 3pi/2 then find the following: sinx, cosx, cotx, secx, and cscx

Question

Hint: (draw a triangle in the correct quadrant, then use pythagoren theorem to find the missing side)

Please help. This is for my ap calc summer packet and i have no clue what it means

Answer 1

So if the tangent of x is 5/2 then the lengths of 2 sides of the triangle are 5 and 2 and the third is √29

Pythagorean theorem: a^2+b^2=c^2

so 5^2+2^2=29

so c=√29

 

Because pi≤x≤3/2*pi we know we are in the third quadrant (bottom left). So the triangle would trace 2 spaces in the negative x direction and 5 spaces in the negative y direction with the hypotenuse connecting the origin to the point (-2,-5).

 

Also we know the angle corresponding with the vertex on the origin is 68.2 degrees (tan^-1(5/2)). From this information, you should be able to find the sin, cos, cot, sec, csc of x. Make sure that the values you find have the correct sign (positive or negative).

Answer 2

This can be determined using a quadrant III triangle. Opposite side (y) is -5 and adjacent side (x) is -2.  Hypotenuse is sqrt(29).

 

sin = -5/sqrt(29)

cos = -2/sqrt(29)

tan = 5/2