# Calculate sin75 without calculator

1. Sep 2, 2015

### Robin04

1. The problem statement, all variables and given/known data
Calculate sin75 without calculator!

2. Relevant equations

3. The attempt at a solution
I constructed a triangle with angles 15, 75 and 90 then I defined sin75 by the sides. In a previous exercise the task was the same but with tg15 and I used the result in this execise too.
I wrote the equation: tg15 = b/a and if I express b and put it in the Pythagorean theorem I get the right result. However, if I express a and put it in the Pythagorean theorem I got a wrong result and I don't know why is this happening. I looked through it and I haven't find any calculation error... The second way is a lot longer but I should work. :(

http://kepfeltoltes.hu/thumb/150902/IMG_0122_www.kepfeltoltes.hu_.jpg

http://kepfeltoltes.hu/thumb/150902/IMG_0123_www.kepfeltoltes.hu_.jpg

Last edited: Sep 2, 2015
2. Sep 2, 2015

### Staff: Mentor

Are you familiar with double angle and half angle formulas? How is sin75 related to cos15? What is cos(2θ) in terms of cosθ?

Chet

3. Sep 2, 2015

### Ray Vickson

You really should type out your work; most helpers here (me included) will ignore any of the details in your post.

I am willing to offer a hint, though: if you look on-line you can find documents that give closed-form formulas for sines or cosines of all angles from 1 degree to 89 degrees in increments of 1 degree.

Last edited: Sep 2, 2015
4. Sep 2, 2015

### Robin04

I haven't learnt them but I have the formulas in my book.

5. Sep 2, 2015

### Hamza Abbasi

• Member warned about posting complete solutions
Break the angle 75 into component angles which are more familiar e.g 15,30 ,45 , then apply sin(alpha+beta) formula...
sin 75
= sin(45 + 30)
= sin45cos30 + cos45sin30
= (½√2)(½√3) + (½√2)(½)
= ¼(√6 + √2)

6. Sep 2, 2015

### Ray Vickson

PF helpers are not allowed to give complete solutions!

7. Sep 2, 2015

### Hamza Abbasi

Oh !! Sorry I didn't knew that , I will try to avoid it in the future.

8. Sep 2, 2015

### Robin04

Thanks for your answer! :) But can you help me with explaining why my solution doesn't work? They seem completely equivalent for me.