If sin⁡ x=12/13, and 0°<x<90°, find cos⁡(x+30°). what is the correct answer

Question

options

−12+5√3/26

+12-5√3/26

12+5√3/26

−12-5√3/26

Answer 1

Hi Jacob:

This is how tackle this type of problem:

Draw a right triangle with the indicated sides: side opposite the angle = 12 and hypotenuse = 13

Then, calculate the 3rd side by Pythagoras: x² + 12² = 13²

x² = 169 - 144

x² = 25

x = 5

Now, we have all 3 sides of our diagram triangle, so we can find all the trig ratios for the angle.

Next, we use the double angle formula to simplify cos(x + 30) = cos x cos 30 - sin x sin 30

= 5/13 . √3/2 - 12/13 . 1/2

= 5√3 /26 - 6/13

= (5√3 - 12) / 26

So answer (a) is correct - although it is missing the parentheses!