# 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/290 ≤ θ ≤ 180 (or) π/2 ≤ θ ≤ π180 ≤ θ ≤ 270 (or) π ≤ θ ≤ 3π/2270 ≤ θ ≤ 360 (or) 3π/2 ≤ θ ≤ 2π θ lies in 1st quadrantθ lies in 2nd quadrantθ lies in 3rd quadrantθ 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.
 θ180 - θ (or) π - θθ - 180 (or) θ - π360 - θ (or) 2π - θ θ lies in 1st quadrantθ lies in 2nd quadrantθ lies in 3rd quadrantθ 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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