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Std X. Trigonometry sheet

Ashish Kashyap
24/04/2018 0 0

For a right angled triangle, with one angle θ (which is not the right angle), the trigonometric ratios are defined as follows:

sin θ = Perpendicular / Hypotenuse  (corresponding to the angle θ)

cos θ = Base / Hypotenuse (corresponding to the angle θ)

tan θ = Perpendicular / Base (corresponding to the angle θ)

Notice that tanθ = sinθ/cosθ.

 

Three other ratios are also defined as the inverse of the basic three ratios.

cosec θ = 1/sinθ

sec θ = 1/cosθ

cot θ = 1/tanθ = cosθ/sinθ

 

By applying the Pythagoras theorem to the right angled triangle, we can deduce the following identities:

  • sin²θ + cos²θ = 1      (use Pythagoras theorem for AB,BC and AC)
  • 1 + cot²θ = cosec²θ  (divide the first identity by sin²θ)
  • 1 + tan²θ = sec²θ     (divide the first identity by cos²θ)

From the right angled triangle, we can also see that if one angle is θ, the other acute angle is (90-θ). Taking the same three ratios for the angle (90-θ), we find that:

sin(90-θ) = cosθ,

cos(90-θ)= sinθ, 

tan(90-θ)=cotθ.

 

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