Trig identities are equations involving trigonometric functions that are true for all values of the variables. Here are some common trig identities that are covered in Grade 11:
1. Pythagorean Identity: sin²Î¸ + cos²Î¸ = 1
This identity shows the relationship between the sine and cosine functions of an angle in a right triangle.
2. Reciprocal Identities:
a. sinθ = 1/cscθ
b. cosθ = 1/secθ
c. tanθ = 1/cotθ
These identities show the relationship between the six trigonometric functions and their reciprocals.
3. Quotient Identities:
a. tanθ = sinθ/cosθ
b. cotθ = cosθ/sinθ
These identities express the tangent and cotangent functions in terms of sine and cosine functions.
4. Co-function Identities:
a. sin(π/2 - θ) = cosθ
b. cos(π/2 - θ) = sinθ
c. tan(π/2 - θ) = cotθ
d. cot(π/2 - θ) = tanθ
These identities show the relationship between complementary angles and their trigonometric functions.
5. Even-Odd Identities:
a. sin(-θ) = -sinθ
b. cos(-θ) = cosθ
c. tan(-θ) = -tanθ
These identities show how the sine, cosine, and tangent functions behave under changes of sign or parity.
6. Sum and Difference Identities:
a. sin(A+B) = sinAcosB + cosAsinB
b. cos(A+B) = cosAcosB - sinAsinB
c. tan(A+B) = (tanA + tanB) / (1 - tanAtanB)
These identities express the sine, cosine, and tangent of the sum or difference of two angles in terms of the sine, cosine, and tangent of the individual angles.
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