Question

Help please...Cosθ=-2/7 and tanθ<0. Find cscθ

Answer 1

Cos(x)=-2/7 happens at 2 locations, quad. 2 and 3 (this is when cos is negative). Since we know that tan(x)<0 (which is to say tan(x) is negative), and that tan(x)=sin/cos, thus, that ONLY when you divide a negative by a positive value, will you get a negative value, that sin HAS to be positive, therefore, the value is in quad. 2. Now, just take the inverse cos of (-2/7) (make sure that the degree (or radii) falls in the 2 quad), and put that value under 1:\[\cos(\theta)=-2/7\rightarrow \theta = \cos^{-1} (-2/7)\]
Put that value under 1:\[1/(Value That You Found)\]

Answer 2

It's in the second quadrant because cos is x/r. r is the hypotenuse and can't be negative so the x is negative. and since tangent is less than zero it's negative. Tangent can only be negative in the 2nd and 3rd quadrant.

Anyway, solve for the missing side. Since you are looking for the csc, first you need to find the sin of the angle. To get the csc, just flip the sin.

Does that help?

Answer 3

yes it help thank you to both of you.