# Sine function in equation issue

1. Apr 1, 2016

### Einstein's Cat

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >

Say one has the equation of
90= Sin^-1(a) + Sin^-1(b), how would one made the term "b" the subject of such an equation? Please excuse any naivety.

Last edited by a moderator: Apr 1, 2016
2. Apr 1, 2016

### micromass

1) This belongs in the homework forum
2) You should provide an attempt at the solution.

3. Apr 1, 2016

4. Apr 1, 2016

### Staff: Mentor

@Einstein's Cat -- Where are you getting these math questions from? Is it for schoolwork? Or are you trying to self-study math on your own?

Also, it would help a lot if you would read the tutorial on how to use LaTeX (see Help/How-To under INFO at the top right of the page). It would make it much easier for us to parse the equations you are trying to type into the forum. I'm not sure how to try to parse what you have written above...

5. Apr 1, 2016

### Einstein's Cat

It is self- study maths and thank you for the advice

6. Apr 1, 2016

### Staff: Mentor

Why don't you read the LaTeX tutorial, and then show us the equation that you are asking about in LaTeX form. Then also show us what steps you think might be useful for trying to manipulate the equation to isolate the variable you want. Please always show your best efforts when asking questions here at the PF.

7. Apr 1, 2016

### Staff: Mentor

Since it is for self-study, it is schoolwork-like. So I will move the thread to the Homework Help forums, where such threads should go.

8. Apr 1, 2016

### HallsofIvy

A pretty obvious answer is that $b= Sin(90- Sin^{-1}(a))$ but that probably isn't what you want-surely you saw that..

9. Apr 2, 2016

### Einstein's Cat

That is indeed what I was wanting and so thank you very much for I am completely ignorant of rearranging sin functions in algebraic terms

10. Apr 2, 2016

### haruspex

But you can simplify it much more, getting rid of the trig functions entirely.
What is a simpler way of writing sin(90o-x)?

11. Apr 2, 2016

### Einstein's Cat

I believe Sin(90) is equal to 1

12. Apr 2, 2016

### haruspex

Yes, but that doesn't help. Consider a right-angled triangle. Let x be one of the other angles. What is the third angle?
Can you find two sides with a ratio of sin(90-x)?

13. Apr 3, 2016

### Einstein's Cat

The other angle would equal 180 -(90+x) and I'm sorry but I do not know the answer to your final question

14. Apr 3, 2016

### haruspex

Consider a triangle ABC. Angle at C is a right angle, so AB is the hypotenuse. Consider angle at A. The sine of A is the ratio of two sides of the triangle. Which two sides? Which ratio is the cosine?