# Can someone help me answer this question? 'find the exact value of Cos theta, given sin theta = 5/9 and cos theta < 0

##### 3 Answers

I got

#### Explanation:

Have a look:

= -0.8315 (4dp)

#### Explanation:

Find **(Note: there are 2 possible angles for #sin(theta) = 5/9 #)**

The sin will also have the value

If you are not sure which of these angles will have cos < 1, try both.

(note that the numbers for both angles are actually the same but one is positive and the other is negative)

(so

#### Explanation:

#"using the "color(blue)"trigonometric identity"#

#•color(white)(x)sin^2theta+cos^2theta=1#

#rArrcostheta=+-sqrt(1-sin^2theta)#

#"given "sintheta=5/9" and "costheta<0#

#"then "theta" is in the second quadrant"#

#costheta=-sqrt(1-(5/9)^2)#

#color(white)(costheta)=-sqrt(1-25/81)#

#color(white)(costheta)=-sqrt(56/81)=-sqrt56/9#