Question

Find cot theta, cos theta, sec theta,

Answer 1

we would here like to find out the values of given trigonometric ratios . A right angled triangle is given to us with perpendicular= 3 and hypotenuse= 8

Firstly by Pythagoras theorem, we have ,

`\longrightarrow h^2 = p^2 + b^2\\`

`\longrightarrow 8^2 = 3^2 + b^2 \\`

`\longrightarrow 64 = 9 + b^2\\`

`\longrightarrow b^2 = 64 -9 = 55\\`

`\longrightarrow b =√(55)\approx 7.41`

now as we know that,

`\longrightarrow \cos\theta = (base)/(hypotenuse)=(7.41)/(8)\\`

`\longrightarrow \underline{\underline{ \cos\theta = 0.92 \approx 1}}`

And ,

`\longrightarrow \cot\theta =(base)/(perpendicular)=(7.41)/(3)\\`

`\longrightarrow \underline{\underline{\cot\theta = 2.47 \approx 2 }}`

Finally,

`\longrightarrow \sec\theta =(hypotenuse)/(base)=(8)/(7.41)\\`

`\longrightarrow \underline{\underline{\sec\theta = 1.07 \approx 1 }}`

and we are done!