Answer:
[tex]\sin(1395)=-\frac{\sqrt 2}{2}\\\cos(1395)=\frac{\sqrt 2}{2}\\\tan(1395)=-1[/tex]
Step-by-step explanation:
First, instead of doing 1395, let's find its coterminal angles. We can do so by subtracting 360 until we reach a solvable range. So:
[tex]1395-360=1035[/tex]
This is still too high, continue to subtract:
[tex]1035-360=675\\675-360=315\\315-360=-45[/tex]
So, instead of 1395, we can use just -45.
So, evaluate each trig function for -45:
1)
[tex]\sin(1395)=\sin(-45)[/tex]
Remember that we can move the negative inside of the sine outside. So:
[tex]=-\sin(45)[/tex]
Remember the sine of 45 from the unit circle:
[tex]=-\frac{\sqrt2}{2}[/tex]
2)
[tex]\cos(1395)=\cos(-45)[/tex]
Remember that we can ignore the negative inside of a cosine function. So:
[tex]=\cos(45)[/tex]
Evaluate using the unit circle:
[tex]=\frac{\sqrt 2}{2}[/tex]
Now, remember that tangent is sine over cosine. So: "
[tex]\tan(1395)=\tan(-45)=\frac{\sin(-45)}{\cos(-45)}[/tex]
We already know them. Substitute:
[tex]=\frac{-\frac{\sqrt 2}{2}}{\frac{\sqrt 2}{2}}[/tex]
Simplify:
[tex]=-1[/tex]
And we're done!
