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

2 Answers

4 votes

Answer:

sin135° =
(1)/(√(2) )

Explanation:

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

sin135°

= sin(180 - 135)°

= sin45°

=
(1)/(√(2) ) =
(√(2) )/(2) ← exact value

User Mighty Badaboom
by
4.4k points
5 votes

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

User OceanBlue
by
4.6k points