Question

Find the following trig functions using their reference angles. 13) sin 135°

Answer 1

Answer:

sin135° = $\frac{1}{\sqrt{2} }$

Step-by-step explanation:

135° is in the second quadrant where sin x ° > 0

sin135°

= sin(180 - 135)°

= sin45°

= $\frac{1}{\sqrt{2} }$ = $\frac{\sqrt{2} }{2}$ ← exact value

Answer 2

Answer:

Well, I guess you could use a special representation of the function through a sum of terms, also known as Taylor Series.

It is, basically, what happens in your pocket calculator when you evaluate, for example,  

sin

(

30

°

)

.

Your calculator does this:

sin

(

θ

)

=

θ

−

θ

3

3

!

+

θ

5

5

!

−

...

where  

θ

must be in RADIANS.

In theory you should add infinite terms but, depending upon the accuracy required, you can normally stop at three terms.

In our case we have:  

θ

=

π

6

=

3.14

6

=

0.523

and:

sin

(

π

6

)

=

sin

(

0.523

)

=

0.523

−

0.024

+

3.26

⋅

10

−

4

−

...

=

0.499

≈

0.5