Originally Posted by
RD33 (1 pt) Find the exact value (NO DECIMALS) of each expression by sketching a triangle:
A) sin(cos^-1(3/5))
b) cos(sin^-1(4/5))
I have no idea where to start
A)
Use the fact thatcos^2(x)+sin^2(x) = 1
We have cos^-1(3/5) <=> cos(x) = 3/5 => cos^2(x) = 9/25
Using the trigonometric one we get9/25+sin^2(x) = 25/25 <=> sin^2(x) = 16/25 <=> sin(x) = +/- 4/5
But since cos^-1 is defined for 0 to pi, the only solution is sin(x) = 4/5
By this we now have the expressionsin(cos^-1(3/5)) = sin(sin^-1(4/5)) = 4/5
I leave the second one as exercise for you!