Question

Consider the equation tan(270° + 0)= 1 - sin∅/cos∅ where 0° <∅ < 360°

(a) Rewrite the equation in terms of sin ∅ only.

(b) Hence solve the equation for 0° < ∅ < 360°.​

Answer 1

`\\ \sf\longmapsto tan(270+\theta)=1-(sin\theta)/(cos\theta)`

`\\ \sf\longmapsto (sin(270+\theta))/(cos(270+\theta))=1-(sin\theta)/(cos\theta)`

`\\ \sf\longmapsto (-cos\theta)/(sin\theta)=1-(sin\theta)/(cos\theta)`

`\\ \sf\longmapsto(sin\theta)/(cos\theta) (-cos\theta)/(sin\theta)=1`

`\\ \sf\longmapsto (sin^2\theta-cos^2\theta)/(-cos\theta sin\theta)=1`

`\\ \sf\longmapsto (-2cos\theta)/(-cos\theta sin\theta)`

`\\ \sf\longmapsto (2)/(sin\theta)=1`

`\\ \sf\longmapsto 2cosec\theta=1`

`\\ \sf\longmapsto cosec\theta=(1)/(2)`

`\\ \sf\longmapsto \theta=cosec^(-1)\left((1)/(2)\right)`

• theta doesn't exist