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Unlocking the Power of Trig Identities: Grade 11 Students' Ultimate Guide to Mathematical Mastery!

Trig identities grade 11


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: sin²θ + cos²θ = 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.

Here are some General solutions for trigonometry


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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