Question

For which acute angle are the sine of the angle and cosine of the angle equal? 30º 45º 60º 75º

Answer 1

Hello

sin ..... | 0° |30°|45°|60°|90°|
...........| 0...| 1..| 2..|  3..| 4..|  write numbers
...........| 0...| 1..|√2.| √3 | 2..| take root square
...........| 0...|1/2|√2/2|√3/2|1| divide by 2
...........| 0...|1/2|√2/2|√3/2|1| .....
cos.....| 90°|60°|45°|30°| 0°|

sin (75°)
=sin(30°+45°)=sin 30°*cos 45° +cos 30°*sin 45°
....................  =1/2*√2/2            +  √3/2*√2/2
....................   = √2(1+√3)/4

cos 75°
=cos(30°+45°)=cos 30°*cos 45°-sin 30°*cos 45°
=√3/2*√2/2-1/2*√2/2
=√6/4-√2/4=√2/4*(√3 -1 )