What is the answer for question 8) ?

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a) Given `costheta=1/sqrt10`

Therefore, `sintheta=sqrt(1-cos^2theta)`

`=sqrt(1-1/10)`

`=sqrt(9/10)`

`=3/sqrt10 ` (Note that if theta is a first quadrant angle, then the value of sintheta must be positive, so the negative root is discarded).

b) Given `tanbeta=-sqrt5/2`

Therefore, `secbeta=sqrt(1+tan^2beta)`

`=sqrt(1+5/4)`

`=sqrt(9/4)`

`=-3/2` (Note that if beta is a second quadrant angle, then the value of cosbeta, and secbeta must be negative, so the positive root is discarded).

Hence `cosbeta=1/secbeta`

`=1/(-3/2)=-2/3`

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