Question

Using the identity sin2a+cos2a=1 find the value of sins to the nearest hundredth, if cosa= -0.25 and pi/2<0

Answer 1

Given data:

The given value of cos(θ)= -0.25.

The value of sin(θ) is,

`\begin{gathered} \cos ^2(\theta)+\sin ^2(\theta)=1 \\ \sin ^2(\theta)=1-\cos ^2(\theta) \\ \sin (\theta)=\sqrt[]{1-(-0.25)^2} \\ =\sqrt[]{1-0.0625} \\ =0.968 \\ \approx0.97 \end{gathered}`

The value of sine function is positive in the second quadrant tha is when θ lies between π/2 to π.

Thus, the value of sin(θ) is 0.97.