Question

Find the function value. tan495°

Answer 1

Answer: -1

Step-by-step explanation:

You want to find an angle that is coterminal to 495. So, subtract 360 degrees until youre in the range of 0-360. I got 495 - 360 = 135°

Tangent is equal to $\frac{sin(theta)}{cos(theta)}$, we already solved theta which was 135°

This next part is hard to explain to someone who doesnt know their trig circle, idk if you do. The angle 135 is apart of the pi/4 gang. So we know this is going to be some variant of √2/2. Sine of quadrant 1 and 2 is gonna be positive:

$sin135=\frac{\sqrt{2} }{2}$

Now lets do cosine of 135°, which again is apart of the pi/4 gang because its divisible by 45°. Its in quadrant 2 so the cosine will be negative.

$cos135=-\frac{\sqrt{2} }{2}$

The final step is to divide them. They are both fractions so you should multiply by the reciprocal.

$\frac{\sqrt{2} }{2} *-\frac{2}{\sqrt{2} } =-\frac{2\sqrt{2} }{2\sqrt{2} } =-1$

Answer 2

-1
The answer is -1