What is the Trigonometric Value of cos θ = -2/3, 90º < θ < 180º; sin θ?
2 Answers
Feb 20, 2018
Explanation:
#"using the "color(blue)"trigonometric identity"#
#•color(white)(x)sin^2theta+cos^2theta=1#
#rArrsintheta=+-sqrt(1-cos^2theta)#
#"since "90^@ < theta<180^@#
#"then "theta" in second quadrant where "sintheta>0#
#sintheta=sqrt(1-(-2/3)^2)#
#color(white)(sintheta)=sqrt(5/9)=sqrt5/3#
Feb 20, 2018
See explanation.
Explanation:
The task is to calculate
#sin^2theta+cos^2theta=1#
If we substitute the given data we get:
#sin^2theta+(-2/3)^2=1#
#sin^2theta+4/9=1#
#sin^2theta=1-4/9#
#sin^2theta=5/9#
This equation has 2 solutions:
To decide which value is correct we have to use the information given. If the angle is in the 2nd quadrant (