How do you calculate which angles have the same ratios?

[bushra1175]

Hi everyone. I came across these questions and I couldn't determine from the textbook how this is worked out. Here are the questions and solutions. What method do you use to work out, for example, what other angles have the same sine as sine 50 degrees? Question a and b are both worked out by taking away theta from 180. But this isn't used in the other questions so I couldn't see the pattern.

 

[Deleted member 4993]

Hi everyone. I came across these questions and I couldn't determine from the textbook how this is worked out. Here are the questions and solutions. What method do you use to work out, for example, what other angles have the same sine as sine 50 degrees? Question a and b are both worked out by taking away theta from 180. But this isn't used in the other questions so I couldn't see the pattern.

View attachment 21208 View attachment 21209

You should be familiar with the following identities:

for 0 <= x <= 2pi

sin(x) = sin(pi - x)

cos(x) = cos(-x)

tan(x) = tan(pi + x) .....................................etc,

If you are not, open your trig text-book and get familiar.

 

[bushra1175]

You should be familiar with the following identities:

for 0 <= x <= 2pi

sin(x) = sin(pi - x)

cos(x) = cos(-x)

tan(x) = tan(pi + x) .....................................etc,

If you are not, open your trig text-book and get familiar.

I found these identities so I understand now. Thanks

 

[Dr.Peterson]

I found these identities so I understand now. Thanks

View attachment 21210

Those aren't quite the ones you need; I would expect your list to start with [MATH]\sin(\theta) = \sin(180^\circ-\theta)[/MATH], which is what they used for the first example.

 

[Steven G]

I personally do not remember many of those identities but knowing where each trig function is positive and negative and using reference angles I can do most of the problems you were given. The remaining ones I can do by knowing the graph of the sine and cosine functions. Instead of memorizing these identities it is much easier to see them! That is true understanding.