Question

If angle θ is in standard position and the terminal side of θ intersects the unit circle at the point 1/
`(1/√(10), -3/√(10))`

find sin θ, cos θ,and tan θ.

sin θ =


cos θ =


tan θ =

Answer 1

Explanation:

REcall that all the points of the unit circle have the following coordinates
`(\cos \theta, \sin \theta)`, where theta is the angle in standard position (that is, with the terminal side on the given point and the initial side on the x-axis).

Then in this case we have that
`\cos\theta = \frac{1}{\sqrt[]{10}}, \sin \theta =\frac{-3}{\sqrt[]{10}}`.

Recall that
`\tan \theta = (\sin \theta)/(\cos \theta) = \frac{\frac{-3}{\sqrt[]{10}}}{\frac{1}{\sqrt[]{10}}} = -3`