To evaluate the trigonometric functions of
csc 59°
sin 23°
cot 6°
sec 11°
To evaluate these trigonometric functions, first we must remember the definitions of the trigonometric functions:
csc(theta) = 1/sin(theta)
sin(theta) = opposite/hypotenuse
cot(theta) = 1/tan(theta) = adjacent/opposite
sec(theta) = 1/cos(theta)
Now, let's evaluate each function:
csc 59° = 1/sin 59°
sin 59° = opposite/hypotenuse
By using Pythagorean identities, we find:
opposite = sqrt(1^2 - cos^2 59°) = sqrt(1 - cos^2 59°)
hypotenuse = 1
Therefore, sin 59° = sqrt(1 - cos^2 59°)/1
So, csc 59° = 1/sqrt(1 - cos^2 59°)
sin 23° = opposite/hypotenuse
By using Pythagorean identities, we find:
opposite = sqrt(1^2 - cos^2 23°) = sqrt(1 - cos^2 23°)
hypotenuse = 1
Therefore, sin 23° = sqrt(1 - cos^2 23°)/1
cot 6° = 1/tan 6°
tan 6° = opposite/adjacent
By using Pythagorean identities, we find:
opposite = sqrt(1^2 - cos^2 6°) = sqrt(1 - cos^2 6°)
adjacent = 1
Therefore, tan 6° = sqrt(1 - cos^2 6°)/1
So, cot 6° = 1/sqrt(1 - cos^2 6°)
sec 11° = 1/cos 11°
These are the evaluations of the given trigonometric functions.