Question

Given sin(theta)= 7/11 and sec(theta)<0 Find cos(theta) and tan(theta)

Answer 1

Answer:

cos∅ = $-\frac{6\sqrt{2} }{11}$

Step-by-step explanation:

Answer 2

When given a trigonometric ratio, and asked to find another ratio, we draw a right triangle as shown in the picture.

From the pythagorean theorem we find the length of AB:

 $|AB|= \sqrt{ AC^{2}- BC^{2} }= \sqrt{ 11^{2}- 7^{2} }= \sqrt{121-49} = \sqrt{72} = \sqrt{2*36}$ $= 6\sqrt{2}$

the numerical value of

cos∅=adjacent side/hypotenuse=$\frac{ 6 \sqrt{2} }{11}$

since sec∅=1/cos∅, and sec∅ is negative, then cos∅ is also negative.


Answer: 

cos∅=$-\frac{ 6 \sqrt{2} }{11}$