Question

Let , −5−6 be a point on the terminal side of θ . find the exact values of cosθ , cscθ , and tanθ .

Answer 1

Given that point (-5, -6) is a point on the terminal side of θ. Since both the x coordinate and the y-coordinate are negative, θ is in the third quadrant.

The side opposite θ is -6 and the side adjacent θ is -5.

The hypothenus is given by
`√((-6)^+(-5)^2)=√(36+25)=√(61)`

The exact value of cosθ is given by:


`\cos\theta= (adjacent)/(hypothenuse) = (-5)/(√(61))`

The exact value of cscθ is given by:


`\csc\theta= (hypothenuse)/(opposite) = (√(61))/(-6)`

The exact value of tanθ is given by:


`\tan\theta= (opposite)/(adjacent) = (-6)/(-5) =1.2`