Question

Question #430a4

Answer 1

Please see below.

Explanation:

.

Poinr `P` has the coordinates `(-3,4)`

Connecting `P` to `O`, the origin, and drawing a vertical line from `P` to the `x`-axis where the line intersects the `x`-axis at point `M`, makes triangle `DeltaPMO` which is a right triangle, i.e. `/_PMO= 90^@`.

`PM=4`

`OM=-3`

We can use the Pythagorean formula to calculate `PO`

`(PO)^2=(PM)^2+(OM)^2`

`(PO)^2=4^2+(-3)^2=16+9=25`

`PM=5`

By definition,

`sintheta=("Opposite")/("Hypotenuse")=(PM)/(PO)=4/5=0.8`

`costheta=("Adjacent")/("Hypotenuse")=(OM)/(PO)=-3/5=-0.6`

`tantheta=("Opposite")/("Adjacent")=(PM)/(OM)=4/-3=-1.33`