Complementary Angles In Trigonometry





In this page complementary angles in trigonometry we are going to see all complementary angles using trigonometric ratios.

  1. sin (90 - θ) = cos θ
  2. cos (90 - θ) = sin θ
  3. tan (90 - θ) = cot θ
  4. cot (90 - θ) = tan θ
  5. cosec (90 - θ) = sec θ
  6. sec (90 - θ) = cosec θ 

Now we are going to see the example problems based on the above formulas.

Example problems using complementary angles in trigonometry

Example 1:

Evaluate  (tan 65°)/ (cot 25°)

Solution:

In this problem we are going to use the identity tan (90 - θ) = cot θ

  tan 65° = tan ( 90 - 25° )

  tan 65° = cot 25°

             =  (tan 65°)/ (cot 25°)

             =  (cot 25°)/(cot 25°)

             =   1


Example 2:

Evaluate  sin 20° tan 60° sec 70°

Solution:

  sec 70° = sec ( 90 - 20° ) = cosec  20°

   cosec  20° = 1/(sin 20°)

  sin 20° tan 60° sec 70°

             =  sin 20° tan 60° cosec  20°

Now we are going to apply 1/(sin 20°) instead of cosec 20°

             =  sin 20° tan 60° x  [1/(sin 20°)]

sin 20° which are in both numerator and denominator will get canceled.

             =  tan 60°

the value of tan 60° is

             =  √3


Example 3:

Evaluate  (sin 36°)/ (cos 54°)

Solution:

In this problem we are going to use the identity sin (90 - θ) = cos θ

   sin 36° =  sin ( 90 - 54° )

   sin 36°  =  cos  54°

             =  (sin 36°)/ (cos 54°)

             =  (cos 54°)/(cos 54°)

             =   1


Example 4:

Evaluate  (tan 35°)/ (cot 55°)

Solution:

In this problem we are going to use the identity tan (90 - θ) = cot θ

   tan 35° =  tan ( 90 - 55° )

   tan 35° =  cot  55°

              =  (tan 35°)/ (cot 55°)

              =  (cot 55°)/ (cot 55°)

             =   1


Example 5:

Evaluate  3 (sin 23°/cos 67°) + 4(sec 47°/cosec 43°)

Solution:

   sin 23° =  sin ( 90 - 67° )

   sin 23° =  cos 67° 

   sec 47° = sec (90-43°)

   sec 47° = cosec 43°

              = 3 (cos 67°/cos 67°) + 4(cosec 43°/cosec 43°)

              = 3(1) + 4(1) 

              = 3 + 4

              = 7


Example 6:

Evaluate  sin θ sec (90° - θ)

Solution:

             = sin θ cosec θ

            = sin θ x (1/sin θ)

            = 1



  1. Trigonometric Ratios
  2. Trigonometric Identities
  3. Values Of Certain Angles
  4. Heights and distance
  5. Double Angle Formulas
  6. Half Angle Formulas
  7. Compound Angle Formulas
  8. 3A formulas
  9. Compound angles sum and differences
  10. Sum to product forms
  11. Trigonometry Problems Using Identities
  12. Trigonometry Practical Problems

HTML Comment Box is loading comments...








Complementary Angles In Trigonometry to Trigonometry