Using the reference angle to evaluate trigonometric functions.
Problem 1 :
Problem 2 :
Problem 3 :
Problem 4 :
1. Answer :
The angle 240° has its terminal side in quadrant III, as shown in figure below.
The reference angle is therefore
240° - 180° = 60°,
and the value of sin 240° is negative. Thus
sin 240° = -sin 60° = √3/2
2. Answer :
The angle 495° is coterminal with the angle 135°, and the terminal side of this angle is in quadrant II, as shown in figure below.
So the reference angle is
180° - 135° = 45°,
and the value of cot 495° is negative. We have
cot 495° = cot 135° = -cot 45° = -1
3. Answer :
The angle 16π/3 is coterminal with 4π/3, and these angles are in quadrant III, as shown in the figure below.
Thus, the reference angle is
4π/3 - π = π/3
Because the value of sine is negative in quadrant III, we have
sin 16π/3 = sin 4π/3 = -sin π/3 = -√3/2
4. Answer :
The angle -π/4 is in quadrant IV, and its reference angle is π/4, as shown in the figure below.
Because secant is positive in this quadrant, we get
sec (-π/4) = +sec (π/4) = √2/2
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