HOW TO FIND EXACT VALUE OF TRIG FUNCTIONS WITHOUT 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.
Problem 1 :
cos -210°
Solution:
cos -210° = cos 210°
= cos (180° + 30°)
= -cos 30°
= -√3/2
Problem 2 :
Solution:
Problem 3 :
Solution:
Problem 4 :
Solution:
Problem 5 :
csc -420°
Solution:
Problem 6 :
cos 1050°
Solution:
cos 1050° = cos (330° + 720°)
= cos (330°)
= cos(360° - 30°)
= cos 30°
= √3/2
Problem 7 :
cot -840°
Solution:
Problem 8 :
Solution:
Problem 9 :
sin -450°
Solution:
sin -450° = - sin(360° + 90°)
= - sin 90°
= -1
Problem 10 :
sin 240°
Solution:
sin 240° = sin (180° + 60°)
= -sin 60°
= -√3/2
Problem 11 :
csc π
Solution:
Problem 12 :
Solution:
Problem 13 :
sec -390°
Solution:
Problem 14 :
cos -930°
Solution:
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