Question

Let , (-2,3) be a point on the terminal side of θ . find the exact values of sinθ , secθ , and tanθ .

Answer 1

Here we have to use the following ratio rule

`tan \Theta =(y)/(x)`

In the given point , x=-2, y=3, so

`tan \Theta =- (3)/(2)`

`sec \theta = √(1+tan^2 \theta)`

Using the value of tan theta, we will get

`sec \theta = -\sqrt{1+(9)/(4)} = -(√(13))/(2)`

Now we need to find the value of cos theta

`cos \theta = -(1)/(sec \theta) = -(2 √(13))/(13)`

And

`sin \theta = √(1-cos^2 \theta) = \sqrt{1-(4)/(13)} =(3 √(13))/(13)`