Exploring Trigonometric Identities

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1. 1

   What is the Pythagorean identity?

   A <b>sin²θ + cos²θ = 1</b> B <b>tan²θ + sec²θ = 1</b> C <b>csc²θ − cot²θ = 1</b>
2. 2

   How is the tangent of an angle expressed in terms of sine and cosine?

   A <b>tanθ = sinθ * cosθ</b> B <b>tanθ = cosθ / sinθ</b> C <b>tanθ = sinθ / cosθ</b>
3. 3

   Which of these is an expression for the sine of a sum of two angles (A + B)?

   A <b>sin(A + B) = sinA sinB + cosA cosB</b> B <b>sin(A + B) = sinA cosB + cosA sinB</b> C <b>sin(A + B) = cosA / cosB + sinA / sinB</b>
4. 4

   What is the double angle formula for cosine?

   A <b>cos(2θ) = 2sin²θ - 1</b> B <b>cos(2θ) = sin²θ - cos²θ</b> C <b>cos(2θ) = cos²θ - sin²θ</b>
5. 5

   Which function is the reciprocal of the sine function?

   A <b>cosecant (csc)</b> B <b>secant (sec)</b> C <b>cotangent (cot)</b>
6. 6

   What is the value of sin(90°)?

   A <b>1</b> B <b>0</b> C <b>-1</b>
7. 7

   Which trigonometric identity represents cos²θ in terms of sin²θ?

   A <b>cos²θ = 1 - tan²θ</b> B <b>cos²θ = tan²θ - 1</b> C <b>cos²θ = 1 - sin²θ</b>
8. 8

   What is the formula for cotangent in terms of other trigonometric functions?

   A <b>cotθ = tanθ</b> B <b>cotθ = 1/tanθ</b> C <b>cotθ = tan²θ - 1</b>
9. 9

   What identity is derived from the double angle formula for sine?

   A <b>sin(2θ) = 2cos²θ - 1</b> B <b>sin(2θ) = cos²θ - sin²θ</b> C <b>sin(2θ) = 2sinθcosθ</b>
10. 10

    Which function is not a fundamental trigonometric function?

    A <b>sine (sin)</b> B <b>cosine (cos)</b> C <b>inverse cotangent (cot⁻¹)</b>