Question

Question Below.

Answer 1

I have about 12 practice questions. Here is # 1.

\[\sin(45-\theta)=\sqrt{2/2}\](____)

cos θ+sin θ
cos θ-sin θ
sin θ- cos θ
sin θ-cos θ

Answer 2

I do not even know where to begin in completing the problem.

Answer 3

do you know for what angle \(\sf\Large sin ~\theta = \frac{\sqrt{2}}{2}\)

Answer 4

And I have no clue what those last four lines are... answer choices? o.O

Answer 5

I do not.

Answer 6

well... umm.. use the unit circle?

https://www.mathsisfun.com/geometry/images/circle-unit-304560.gif

The x-coordinate is the cos value for the angle, and the y-coordinate is the sin value for the angle

Answer 7

yes they are answer choices.

Answer 8

In that case, I have no clue what your question is really asking. If it was asking for what theta was, then I can understand but otherwise no clue

Answer 9

maybe which answer choice makes it an identity?

Answer 10

oh, I see now

this is what we have to use:

sin(A − B) = sin A cos B − cos A sin B

and hint: sin45 = sqrt(2)/2 and cos45 = sqrt(2)/2

Answer 11

so what do we substitute? Do I use sqrt(2)/2? Sorry I just started this course yesterday.

Answer 12

we start with the left hand side. Plug in 45 for A and \(\theta\) for B and open it up :)

Answer 13

so then we get \[\sqrt{2\cos \theta}/2 - \sin(\theta)\sqrt{2}/2\]

Answer 14

oops but the cos theta is not under the sqrt

Answer 15

yes, now we factor out the sqrt(2)/2 from it

Example:

ab + ac = a( b + c)

this is the distributive formula, but we're using it backwards kind of :P

Answer 16

so do we still use the 45 for a and theta for b?

Answer 17

yes, we currently have:

\(\Large sin(45 - \theta) = \frac{\sqrt{2}}{2}cos\theta - sin\theta \frac{\sqrt{2}}{2}\)

All we have to do is factor \(\Large\frac{\sqrt{2}}{2}\) from the right hand side. :)

Answer 18

oh okay

Answer 19

so I got \[\theta=\pi/4+\pi*\]

Answer 20

I dont think I fully understand what to do sorry

Answer 21

we aren't solving for theta :)

if you factor out the sqrt(2)/2 you'll get your final answer

also a side note, we were given 45 degrees. That means the answer should be kept in degrees (if we were solving for theta)

Answer 22

but none of the answer choices are in degrees

Answer 23

what does that mean

Answer 24

if we were solving for theta, then the answer would have to be degrees since we were given degrees.

Here we aren't solving for theta. We're trying to simplify what sin(45 - theta) is

Answer 25

so what do I have to do to factor correctly?

Answer 26

ab + ac becomes a(b + c)

\(\Large sin(45 - \theta) = \frac{\sqrt{2}}{2}cos\theta -\frac{\sqrt{2}}{2}sin \theta\)

All we have to do is factor \(\Large\frac{\sqrt{2}}{2}\) from the right hand side. :)

Answer 27

so then it becomes cos theta - sin theta right/?

Answer 28

Correct! And that's your answer :D

Answer 29

aw haha thanks a bunch youre super !!

Answer 30

Anytime! :)