EVALUATING TRIG FUNCTIONS WITHOUT A CALCULATOR
In the given trigonometric function, first find the required angle lies in which quadrant.
|
0 ≤ θ ≤ 90 (or) 0 ≤ θ ≤ π/2 90 ≤ θ ≤ 180 (or) π/2 ≤ θ ≤ π 180 ≤ θ ≤ 270 (or) π ≤ θ ≤ 3π/2 270 ≤ θ ≤ 360 (or) 3π/2 ≤ θ ≤ 2π |
θ lies in 1st quadrant θ lies in 2nd quadrant θ lies in 3rd quadrant θ lies in 4th quadrant |
- It will be easy to convert the angle from radian measure to degree measure.
- To convert the radian measure to degree measure, we have to multiply the given radian by 180/π.
- The by drawing a special right triangle with the help of reference angle, we can easily find the exact value of the trigonometric function.
|
θ 180 - θ (or) π - θ θ - 180 (or) θ - π 360 - θ (or) 2π - θ |
θ lies in 1st quadrant θ lies in 2nd quadrant θ lies in 3rd quadrant θ lies in 4th quadrant |
- Use ASTC to fix the signs.
Find the exact value of each trigonometric function.
Problem 1 :
sec -90°
Solution:
Problem 2 :
Solution:
Problem 3 :
Solution:
Problem 4 :
tan 45°
Solution:
= tan 45°
= 1
Problem 5 :
csc 210°
Solution:
Problem 6 :
Solution:
Problem 7 :
sec -60°
Solution:
sec -60° = sec 60°
= sec (90° - 30°)
[sec (90 - θ) = cos θ]
= cos 30°
Problem 8 :
Solution:
Problem 9 :
sin 330°
Solution:
= sin 330°
= sin (360° - 30°)
= -sin(30°)
= -1/2
Problem 10 :
cot -90°
Solution:
= cot -90°
= 0
Problem 11 :
Solution:
Problem 12 :
Solution:
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