Evaluate the following expressions. Write your answer in degree form. Cos^(-1) √3/2

Question

Evaluate the following expressions. Write your answer in degree form. Cos^(-1) √3/2

Answer 1

Cos^(-1)sqr3/2 = 30 degrees or pi/6 radians

the -1 means the inverse of the cosine of sqr3/2

either use a calculator with an inverse trig function

or you may just recognize sqr3/2 is the cosine of the smallest angle of a 30-60-90 right triangle

30 degrees = pi/6. if you write pi/6 that means pi/6 radians, but "radians" is understood, as implicit

cos(x) = the adjacent side over the hypotenuse. Draw a circle with radius =2, with a 30 degree angle. The adjacent side = square root of 3. Cos(x) is then sqr3 divided by 2

cos(x) = sqr3/2

cos(-1)(x) = the angle whose cosine is sqr3/2 = 30 degrees